About the economicinequality among countries international inequality the United States Wealth inequality ... next to high rise commercial buildings in Cochin , India . Economicinequality or wealth and income ... inequalityinequality among countries . The issue of economicinequality is related ... instrument which diminishes economicinequality, progressive taxation , has been demonstrated to be effective ... saez piketty saezAEAPP06.pdf ref It is a contested issue whether economicinequality ... controversy surrounds it s findings. Economicinequality has existed in a wide range of societies ... in individuals abilities to create wealth are all involved in the creation of economicinequality. Economic ... ref There are various Numerical index economics indic es for measuring economicinequality. Inequality ... for economicinequality within societies. These causes are often inter related. Acknowledged factors that impact economicinequality include the labour market innate ability education computerization ... The labour market A major cause of economicinequality within modern market economy market economies ... co workers. This creates an economicinequality in itself. Members may also receive higher ..., population growth and technological change are often blamed for economicinequality. In discussing ... of compression and decreased inequality between skilled and unskilled workers. Economic neoliberalism ... membership is often suspected as one of the causes of economicinequality. John Schmitt and Ben Zipperer .... This leads to economicinequality even in societies with perfect equality in abilities and circumstances ... successful and unsuccessful ventures in a society results in economicinequality even when all ... curve Main Kuznets curve Simon Kuznets argued that levels of economicinequality are in large part ... by a country s monetary policy , can contribute to economicinequality. ref cite news title Monetary ... Many factors constrain economicinequality they may be divided into two classes government sponsored ... more details
Wiktionary inequalityInequality may refer to In mathematics Inequality mathematics Inequalities book Inequalities book 1934 , a mathematics book by G. H. Hardy , J. E. Littlewood , and George Polya G. Polya In healthcare Health disparities Healthcare inequality In economics Economicinequality Income inequality metrics International inequality Income inequality in the United States Wealth inequality in the United States In the social sciences Participation inequality Social inequality Social equality Social stratification disambig da Ulighed es Desigualdad eo Neegala o fr In galit ... more details
Social inequality refers to a situation in which individuals in a society do not have equal social status . Areas of potential social inequality include voting rights , freedom of speech and assembly, the extent of property rights and access to education , health care , quality Housing inequality housing and other social goods. Causes Social inequality is different from economicinequality , though the two are linked. Economicinequality refers to disparities in the distribution of economic assets and income. While economicinequality is caused by the unequal distribution of wealth , social inequality exists because the lack of wealth in certain areas prohibits these people from obtaining the same housing, health care, etc. as the wealthy, in societies where access to these social goods depends on wealth. Social inequality is linked to racial inequality and wealth inequality . The way people behave socially, through racism and other forms of discrimination, tends to trickle down and affect the opportunities and wealth individuals can generate for themselves. Thomas M. Shapiro presents ... tries to demonstrate the level of inequality on the playing field for blacks and whites . One example ... created fewer opportunities for the black family to acquire wealth, producing social inequality. ref ..., David B. 2001. The Past, Present and Future of Social Inequality. Social Stratification Class, Race, and Gender. Second Edition. Colorado Westview Press. ref The degree of inequality in a given reward .... ref name Grusky, David B 2001 See also div col cols 2 Civil rights Educational inequality Gini coefficient Horizontal inequality LGBT social movements Social equality Social justice Social ... articles 2007 oct2007 usa o16.shtml Social inequality in US hits new record http www.wsws.org articles 2008 may2008 ineq m20.shtml Global survey reveals growing anger over social inequality DEFAULTSORT Social Inequality Category Sociology Category Social inequality Category Social systems Category ... more details
seealso Social equality Horizontal inequality is the inequality economical, social or other that does not follow from a difference in an inherent quality such as intelligence, attractiveness or skills for people or profitability for corporations. In sociology, this is particularly applicable to forced inequality between different subcultures living in the same society. In economics, horizontal inequality is seen when people of similar origin, intelligence, etc. still do not have equal success and have different status, income and wealth. Traditional economic theory predicts that horizontal inequality should not exist in a free market. However, horizontal inequality is observed in real and simulated free market systems. The Pareto optimal economy is one traditional approach to the problem. Even in simulated systems, inequality of perfectly identical actors arises, to give the rich and poor . ref Eric Beinhocker. The Origin of Wealth Evolution, Complexity, and the Radical Remaking of Economics. Harvard Business School Press, 2006. ref References reflist Category Sociology Category Socioeconomics Category Income distribution Category Economic problems econ problem stub ... more details
Wirtinger s inequality is either of two inequality mathematics inequalities named after Wilhelm Wirtinger Wirtinger s inequality for functions Wirtinger inequality 2 forms mathdab ... more details
Sen 1999 p. 87 ref Relation to economicinequality Housing inequality is a type of Economicinequality ... of housing inequality by restricting access to Personal finance household wealth . ref Krivo and Kaufman 2004 ref The effects of housing inequality are necessarily related to economicinequality as they greatly ... Inequality to EconomicInequality, in C. Michael Henry ed. Race, Poverty, and Domestic Policy, pp ... York Russell Sage Foundation. DEFAULTSORT Housing Inequality Category Economicinequality ...Housing inequality refers to the differences in the quality of housing that exist within a given society ... aspects of inequality . ref Sen 2004 p. 61 ref The term may apply regionally across a geographic ... racial or social backgrounds. ref Pryce 2009 p. 145 ref Housing inequality is directly related to concepts of Racism in the United States racial inequality , Social inequality , Income inequality in the United States income inequality , and Wealth inequality in the United States wealth inequality ... forces , Housing discrimination , and Housing Segregation . Housing inequality is also often linked .... ref Yinger 2001p. 360 ref Residential inequality is especially relevant to discussions of poverty ... 2001 ref explains urban residential inequality as a result of natural housing market forces. Yinger ..., or both. ref Yinger 2001 p. 363 ref Ultimately these market forces are subject to other socio economic factors as no one cause can explain housing inequality. In the United States, Thomas Shapiro and Jessica ... discrimination within the housing search process. Effects The most direct effect of residential inequality is an inequality of neighborhood amenities. Neighborhood amenities include factors such as the conditions ..., many studies suggest that growing up in a high poverty neighborhood affects social and economic outcomes ... of plans proposed to remedy the negative effects of housing inequality. Such plans include Subsidized ... site housing International housing inequality While the focus of housing inequality has changed over ... more details
Orphan date February 2009 Spatial inequality is the unequal amounts or qualities of resources and services depending on the area or location, such as medical or Social welfare provision welfare . Some communities have a greater range of resources and services and then those that would be able to change that do not live near or associate with tose communities making it almost impossible to change this cycle. The space within the different locations is the clustering of various groups of people who share similar socio economic statuses. Spatial inequality is caused by various reasons, such as religion, culture, or race. Areas of people in poverty will remain that way until various resources and services are introduced. Resources are things such as fresh drinking water. Services include educational institutions and hospitals other health services. unreferenced date July 2007 Category Economics terminology economic term stub Useful Readings on Spatial Inequality and Agglomeration Combes, Mayer and Thisse, Economic Geography The Integration of Regions and Nations Princeton University Press 2008 Chakravorty, Sanjoy 2003 a , Industrial Location in Post reform India Patterns of Inter regional Divergence and Intra regional Convergence , Journal of Development Studies, Vol. 40, No. 2, pp. 120 52. Deichmann, Uwe Somik V. Lall Stephen J. Redding and Anthony J. Venables 2008 , Industrial Location in Developing Countries , The World Bank Research Observer, Vol. 23, No. 2, pp 219 46. Fujita, Masahisa 1996 Economics of Agglomeration , Journal of the Japanese and International Economies, Vol. 10, pp. 339 378. Fujita, Masahisa and Paul Krugman 2004 The new economic geography Past, present and the future ... Returns and Economic Geography , The Journal of Political Economy, Vol. 99, No. 3, pp. 483 499. Lall, Somik V., Jun Koo and Sanjoy Chakravorty 2003 Diversity Matters The Economic Geography of Industry ... V. and Sanjoy Chakravorty 2005 , Industrial Location and Spatial Inequality Theory and Evidence from ... more details
The following pages deal with inequalities due to Mikhail Gromov mathematician Mikhail Gromov Bishop&ndash Gromov inequality Gromov s inequality for complex projective space Gromov s systolic inequality for essential manifolds L vy&ndash Gromov inequality disambig ... more details
In mathematics , Berger inequality may refer to Berger s inequality for Einstein manifolds the Berger&ndash Kazdan comparison theorem . mathdab ... more details
About the inequality between nations inequality within nations economicinequality Image 2000pppratio.gif ... based on data from list of countries by GDP PPP as of May 2005 . International inequality is inequality between countries cf. Milanovic 2002 . EconomicinequalityEconomic differences between ... of thought on economicinequality Main discussion Economicinequality Perspectives regarding economicinequality Perspectives regarding economicinequality . There are various schools of thought regarding economicinequality. Marxism favors an eventual society where distribution is based on an individual ... based on social justice favor a more equal distribution making claims economicinequality weakens ... Classism Development economics Development geography Economic development Economicinequality Male female ... authorlink Robert Barro title Inequality and Growth in a Panel of Countries journal Journal of Economic ... Income distribution Category Economicinequality ... Inequality . Image Exponential Pattern in GDP per capita distribution.PNG thumb 320px Log lin .... The major component of the world s income inequality the global Gini coefficient is comprised by two ... 2,100 million people with an income level under 1,000 PPP . See Milanovic 2001, p. 38 . Economicinequality very closely matches lognormal distribution as one traverses the strata of national ... the economic Wealth economics wealth of developed and developing countries. Richer countries ... inequality peaked approximately in 1970s when world income was distributed bimodally into rich and poor countries with little overlap. Since then inequality have been rapidly decreasing, and this trend ... hVimVzgtD6w ref Comparisons Some of the economic disparities among nations can be better appreciated when rich and poor countries or societies are contrasted. For example, with regard to income inequality ... inequality researchers defined wealth as the value of physical and financial assets minus debts ... more details
feature for gender based inequality. It influences the structure both based on its economic ...Occupational inequality is the unequal treatment of people based on gender or race in the workplace. When researchers study trends in occupational inequality they usually focus on distribution or allocation ... 3E2.0.CO 3B2 1 Tam, T. 1997. Sex Segregation and Occupational Gender Inequality in the United States ... 3ASSAOGI 3E2.0.CO 3B2 1Tam, T. 1997. Sex Segregation and Occupational Gender Inequality in the United ... Effects Occupational inequality greatly affects the socioeconomic status of an individual which is linked .... Work and occupations, 30 4 441 ref If an individual experiences occupational inequality, it may ... 2939 3A3 3C268 3ATIROIC 3E2.0.CO 3B2 4 Carlson, S. 1992. Trends in Race Sex Occupational Inequality ... saw a tremendous decrease in occupational inequality however, in the 1980s and 1990s, it began to rise again. Theories Occupational inequality has historically always been a problem, but could diminish over time, according to Richard A. Miech, who attributes this potential change to economic theory ... in the competitive market by hiring women and minorities, thereby reducing occupational inequality ... over time to other employers in which occupational inequality could decrease nationally. ref .... Work and occupations, 30 4 441 442 ref Other theories and research suggests occupational inequality ... inequality will continue with advancing age. ref http wox.sagepub.com cgi reprint 30 4 440 Miech, R ... occupational inequality increases. Measuring Occupational Inequality The Duncan Socioeconomic Index ... inequality is measured is by the index of dissimilarity D . The equation is as follows D ... to change occupations to make the distributions equal. ref name Chart disimilarity Occupational Inequality and Occupational Segregation Occupational inequality is often linked with occupational segregation ... 378928?cookieSet 1 Huffman, M. and Cohen, P. 2004 Racial Wage Inequality Job Segregation and Devaluation ... more details
In probability and statistics , a correlation inequality is one of a number of inequalities satisfied by the correlation function s of a model. Such inequalities are of particular use in statistical mechanics . Examples include Bell s inequality FKG inequality Griffiths inequality math stub References springer id c c110420 first P.C. last Fishburn Category Probabilistic inequalities Category Statistical inequalities Category Statistical mechanics Category Inequalities ... more details
In mathematics , the Kantorovich inequality is a particular case of the Cauchy Schwarz inequality , which is itself a generalization of the triangle inequality . The triangle inequality states that the length of two sides of any triangle, added together, will be equal to or greater than the length of the third side. In simplest terms, the Kantorovich inequality translates the basic idea of the triangle inequality into the terms and notational conventions of linear programming . See vector space , inner product , and normed vector space for other examples of how the basic ideas inherent in the triangle inequality line segment and distance can be generalized into a broader context. More formally, the Kantorovich inequality can be expressed this way Let math p i geq 0, quad 0 a leq x i leq b text for i 1, dots ,n. math Let math A n 1,2, dots ,n . math Then math begin align & qquad left sum i 1 n p ix i right left sum i 1 n frac p i x i right & leq frac a b 2 4ab left sum i 1 n p i right 2 frac a b 2 4ab cdot min left left sum i in X p i sum j in Y p j right 2 , , X cup Y A n , X cap Y varnothing right . end align math The Kantorovich inequality is used in convergence analysis it bounds the convergence rate of Cauchy s steepest descent . Equivalents of the Kantorovich inequality have arisen in a number of different fields. For instance, the Bunyakovsky inequality , the Wielandt inequality , and the Cauchy&ndash Schwarz inequality are equivalent to the Kantorovich inequality and all of these are, in turn, special cases of the H lder inequality . The Kantorovich inequality is named after Soviet economist, mathematician, and Nobel Prize winner Leonid Kantorovich , a pioneer in the field of linear programming . References MathWorld urlname KantorovichInequality title Kantorovich Inequality PlanetMath urlname KantorovichInequality title Cauchy Schwarz inequality http carbon.cudenver.edu ... inequality External links http www groups.dcs.st and.ac.uk history Mathematicians Kantorovich.html ... more details
refimprove date March 2011 Inequality in Bolivia Data from the World Bank and the United Nations Human Development Report indicate that income inequality in Bolivia has been increasing significantly since 1997. As of 2009, Bolivia had the highest levels of income inequality, as measured through the Gini coefficient Index, among the Latin American Countries. With a Gini Index of 59.2, Bolivia is ranked 7th out of 134 countries with available data. In 2007, the bottom quintile poorest 20 of the population received a mere 2.2 of the national income while the top quintile richest 20 of the population received 59.7 . Further dissection reveals the top decile richest 10 receiving up to 42.7 of the national income. ref Statistical Yearbook for Latin America and the Caribbean 2010, http websie.eclac.cl anuario estadistico anuario 2010 docs Anuario 20Estadistico 2010.pdf ref Indigenous and Non Indigenous Inequality Bolivia is one of the most culturally diverse societies in Latin America, with approximately 35 different ethnic groups. Official figures from the Bolivian Population Census 2001 estimates that approximately 62 of the total population are indigenous in 2001. ref Bolivian Census 2001, Los pueblos ind genas de Bolivia diagn stico sociodemogr fico a partir del censo del 2001, http www.eclac.org cgi bin getProd.asp?xml publicaciones xml 3 23263 P23263.xml&xsl celade tpl p9f.xsl&base celade tpl top bottom.xsl ref However, this majority of the population remain highly marginalized in economic terms and continue to live in extreme poverty. In Bolivia, mean income per capita in indigenous households was about 300 Bolivian Bolivianos per month in 2001 compared with 480 Bolivian Bolivianos for non indigenous households. ref Bolivian Census 2001, Los pueblos ind genas de Bolivia diagn stico sociodemogr fico a partir del censo del 2001, http www.eclac.org cgi bin getProd.asp?xml publicaciones xml 3 23263 P23263.xml&xsl celade tpl p9f.xsl&base celade tpl top bottom.xsl ref This gap ... more details
orphan date May 2010 Wikify date February 2011 Structural inequality has been identified as the bias that is built into the structure of organizations, institutions, governments or, social br networks. sup 1 sup Structural inequality occurs when the fabric of organizations, institutions, governments or social networks contain an embedded bias which provides advantages for some members and marginalizes .... Structural inequality is believed to be an embedded part of the culture of the United States due ... inequality has been encouraged and maintained in the society of the United States through ... maintains structural inequality through such practices as tracking of students, standardized assessment ... Also see social inequality , racism , discrimination , and oppression . Social inequality occurs when ... 3 sup The sorting that occurs in the educational system parallels the hierarchical social and economic ... role. School Finance School finance is another area where social injustice and inequality might exist ... student in the city p. 28 . sup 6 sup Healthcare An identified inequality that negatively ... status, that positively impact the existing inequality. Studies have noted significant correlations ... correlated with cardiovascular disease. sup 7 sup Historical The structural inequality of tracking ... ease the teaching process. Oakes, 1986 sup 10 sup Race, ethnicity, and socio economic class limits ... social and economic structures in society. Schools have a unique acculturative process that helps ... an economic advantage to some stakeholders, such as prestigious universities, that use standardized ... the educational system to identify how race and racism is a part of the structural inequality of the public ... structural inequality Working paper 2009 03. Retrieved May 02, 2010 from http www.yale.edu ciqle CIQLEPAPERS CIQLEWP2009 3.pdf Grob, M. 2003 . Educational systems and perceived social inequality ... 14, 2000. Oakes, J. 1986 . Keep tracking How schools structure inequality. Tracking . Yale University ... more details
In mathematics , a componentwise inequality mathematics inequality is an expression of the form math x,y in real n x preceq y iff x i leq y i forall i 1, ldots,n math ref http www.ee.ucla.edu ee236a lectures lineqs.pdf ref ref http www.stanford.edu class ee364a lectures sets.pdf ref ref http www.ece.ucsb.edu roy classnotes 271a ECE271a lecture3 small.pdf ref The Euclidean vector vector s do not have to be real number real , they can be from any space in which the inequality mathematics inequality relation is defined. References Reflist algebra stub Category Inequalities ... more details
In mathematics, Peetre s inequality, named after Jaak Peetre , says that for any real number t and any Vector space vector s x and y in R sup n sup , the following inequality holds math left frac 1 x 2 1 y 2 right t le 2 t 1 x y 2 t . math References planetmath id 4681 title Peetre s inequality mathanalysis stub Category Linear algebra Category Inequalities km ... more details
globalize date December 2010 Gender inequality refers to the obvious or hidden disparity between individuals ... in numerous dimensions of daily life. Gender inequality stems from distinctions, whether empirically ... of gender inequality, wage discrimination exists between the male and female gender. Historically, gender inequality has favored men over similarly qualified women. ref name Burstein, Paul 1994 Burstein ... of jobs and earnings associated with jobs. Earnings associated with jobs will cause income inequality ... Inequality at Work. Thousand Oaks, CA SAGE Publications, 1995. ref Human capital theories refer to the education ... name autogenerated1 Based on the census data, women occupy the Tertiary sector of economic activity ... gender role s that causes gender inequality. ref Hurst, Charles, E. Social Inequality. 6th. Boston ..., and abilities are controlled for. The inequality effects of the glass ceiling are more prevalent ... barriers from receiving job promotions or income raises, the effects of the inequality of the glass ... as a cause for income disparities and gendered inequality in the workplace. Statistical discrimination ... 2000 Gender Inequality at Work. New York Russell Sage Foundation, 2000. ref The gendered wage gap varies ... to a survey on gender pay inequality by the International Trade Union Confederation , female ... Women s Employment, Education, And Family, American Economic Review, 2006, v96 2,May .... They also suggest that what is required to solve the problem of wage inequality is to change customer ... role in the creation of gender norms. ref Vianello, Mino, and Renata Siemienska. Gender Inequality A Comparative ..., men are pressured into being the primary economic supporter of the home. ref Jacobs, Jerry, and Kathleen Gerson. The Time Divide Work, Family, and Gender Inequality. Cambridge, Mass Harvard ... inequality Structural marginalization Gender inequalities often stem from social structures ... inequality and the resulting gendered wage disparity. Women have traditionally been viewed as being ... more details
Bonnesen s inequality is an inequality mathematics inequality relating the length, the area, the radius of the incircle and the radius of the circumcircle of a Jordan curve . It is a strengthening of the classical isoperimetry isoperimetric inequality . More precisely, consider a planar simple closed curve of length math L math bounding a domain of area math F math . Let math r math and math R math denote the radii of the incircle and the circumcircle. Bonnesen proved the inequality math L 2 4 pi F geq pi 2 R r 2. , math The term math pi 2 R r 2 math in the right hand side is known as the em isoperimetric defect em . Loewner s torus inequality with isosystolic defect is a Systolic geometry systolic analogue of Bonnesen s inequality. References Bonnesen, T. Sur une am lioration de l in galit isop rimetrique du cercle et la d monstration d une in galit de Minkowski, C. R. Acad. Sci. Paris 172 1921 , 1087 1089. Yu. D. Burago and V. A. Zalgaller, Geometric inequalities . Translated from the Russian by A. B. Sosinski . Springer Verlag, Berlin, 1988. ISBN 3 540 13615 0. Category Elementary geometry Category Inequalities ... more details
In mathematics , Schur s inequality mathematics inequality , named after Issai Schur , establishes that for all Nonnegative number non negative real number s x , y , z and a positive number t , math x t x y x z y t y z y x z t z x z y ge 0 math with equality if and only if x y z or two of them are equal and the other is zero. When t is an even positive integer , the inequality holds for all real numbers x , y and z . Proof Since the inequality is symmetric in math x,y,z math we may assume without loss of generality that math x geq y geq z math . Then the inequality math x y x t x z y t y z z t x z y z geq 0 , math clearly holds, since every term on the left hand side of the equation is non negative. This rearranges to Schur s inequality. Extension A generalization of Schur s inequality is the following Suppose a,b,c are positive real numbers. If the triples a,b,c and x,y,z are similarly sorted , then the following inequality holds math a x y x z b y z y x c z x z y ge 0. math In 2007, Romania n mathematician Valentin Vornicu showed that a yet further generalized form of Schur s inequality holds Consider math a,b,c,x,y,z in mathbb R math , where math a geq b geq c math , and either math x geq y geq z math or math z geq y geq x math . Let math k in mathbb Z math , and let math f mathbb R rightarrow mathbb R 0 math be either convex function convex or monotonic . Then, math f x a b k a c k f y b a k b c k f z c a k c b k geq 0 . , math The standard form of Schur s is the case of this inequality where x a , y b , z c , k 1, m m sup r sup . ref Vornicu, Valentin Olimpiada de Matematica... de la provocare la experienta GIL Publishing House Zalau, Romania. ref Notes reflist See also Inequality mathematics Inequality Category Inequalities Category Articles containing proofs fr In galit de Schur ko it Disuguaglianza di Schur ja km vi B t ng th c Schur zh ... more details
Mathanalysis stub In functional analysis , a mathematical discipline, the Szeg inequality or P lya&ndash Szeg inequality , named after George P lya and G bor Szeg , states that if math 1 leq p infty math and math u mathbb R n rightarrow mathbb R text in W 1,p mathbb R n , math then math int mathbb R n nabla u p , d mathcal H n leq int mathbb R n nabla u p , d mathcal H n. math See also G bor Szeg H lder s inequality Category Sobolev spaces it Disuguaglianza di Polya Szego ... more details
Inequality Reexamined is a book by Amartya Sen first published by Harvard University Press . In Inequality Reexamined Amartya Sen evaluates the different perspectives of the general notion of inequality, focusing mainly on his well known capability approach . The author argues that inequality is a central notion to every social theory which have stood on time. For only if this basic feature is satisfied can a social theory which advocates a set of social arrangements be plausible. Taken as granted the inequality ingredient, the crucial question becomes inequality of what? A.Sen answers to this basic question by advocating his preferred notion of equality which is based on the capability to functionings. Functionings and the role of freedom Confusing date January 2008 Functionings are of two kinds elementary ones such as being in good health, nourished, sheltered and the more complex, social ones such as having self respect, taking part in the life of the community etc. Achievement of an individual is the set of these realized functionings. Whereas capability refers to the real options that someone has in order to pursue his subjective functionings who prefers most.Nevertheless inequalities related to class, gender, communities seem to hinter the extent of human freedom and thus decreasing our capability to function. That is why, a good society oughts to mitigate such discriminations, promoting people s freedom which, according to Sen, is the most valuable element of a satisfactory life. Editions cite book author Amartya Sen title Inequality Reexamined publisher Harvard University Press year 1992 isbn 0 674 45255 0 First Hardcover cite book author Amartya Sen title Inequality Reexamined publisher Harvard University Press year 1995 isbn 0 674 45256 9 Paperback Reprint External links Online version http www.oxfordscholarship.com oso public content economicsfinance 0198289286 toc.html Inequality Reexamined , Oxford Scholarship Online Category Philosophy books Category Sociology ... more details
In mathematics , Steffensen s inequality , named after Johan Frederik Steffensen , is an integral inequality mathematics inequality in real analysis. It states that if a , b R is a non negative, monotonic function monotonically decreasing , integrable function and g a , b 0, 1 is another integrable function, then math int b k b f x , dx leq int a b f x g x , dx leq int a a k f x , dx, math where math k int a b g x , dx. math External links MathWorld title Steffensen s Inequality urlname SteffensensInequality Category Inequalities Category Real analysis mathanalysis stub km fi Steffensenin ep yht l ... more details
This disambiguation page had piped links removed by a bot, per WP MOSDAB . If some links do not seem to belong on this page, they may have originally been piped, so please check before removing links. Thanks In mathematics, Bernstein inequality may refer to Bernstein s inequality mathematical analysis Bernstein inequalities probability theory disambig Category Mathematical disambiguation ... more details
In probability theory , Etemadi s inequality is a so called maximal inequality , an inequality mathematics inequality that gives a bound on the probability that the partial sum s of a Finite set finite collection of independent random variables exceed some specified bound. The result is due to Nasrollah Etemadi . Statement of the inequality Let X sub 1 sub , ..., X sub n sub be independent real valued random variables defined on some common probability space , and let 0. Let S sub k sub denote the partial sum math S k X 1 cdots X k . , math Then math mathbb P left max 1 leq k leq n S k geq 3 alpha right leq 3 max 1 leq k leq n mathbb P left S k geq alpha right . math Remark Suppose that the random variables X sub k sub have common expected value zero. Apply Chebyshev s inequality to the right hand side of Etemadi s inequality and replace by 3. The result is Kolmogorov s inequality with an extra factor of 27 on the right hand side math mathbb P left max 1 leq k leq n S k geq alpha right leq frac 27 alpha 2 mathrm Var S n . math References cite book last Billingsley first Patrick title Probability and Measure publisher John Wiley & Sons, Inc. location New York year 1995 isbn 0 471 00710 2 Theorem 22.5 cite journal last Etemadi first Nasrollah title On some classical results in probability theory journal Sankhy Ser. A volume 47 year 1985 pages 215&ndash 221 id MR 0844022 . JSTOR 25050536 Category Probabilistic inequalities Category Statistical inequalities ... more details
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