# inequality

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**Discourse on Inequality**— Frontispiece and title page of an edition of Rousseau s Discourse on Inequality (1754), published by Marc Michel Rey in 1755 in Holland. Discourse on the Origin and Basis of Inequality Among Men (Discours sur l origine et les fondements de l… …82

**Kolmogorov's inequality**— In probability theory, Kolmogorov s inequality is a so called maximal inequality that gives a bound on the probability that the partial sums of a finite collection of independent random variables exceed some specified bound. The inequality is… …83

**Loomis-Whitney inequality**— In mathematics, the Loomis Whitney inequality is a result in geometry, which in its simplest form, allows one to estimate the size of a d dimensional set by the sizes of its ( d ndash; 1) dimensional projections. The inequality has applications… …84

**Gender inequality**— refers to the obvious or hidden disparities among individuals based on performance of gender (gender can separate from biological sex, see Sex/gender distinction). Gender has been construed as socially constructed through social interactions as… …85

**Healthcare inequality**— (also called health disparities in some countries) refers to the disparities in the access to adequate healthcare between different gender, race, and socioeconomic groups. In the United States, women are more likely to have access to adequate… …86

**Bernoulli's inequality**— In real analysis, Bernoulli s inequality is an inequality that approximates exponentiations of 1 + x .The inequality states that:(1 + x)^r geq 1 + rx!for every integer r ge; 0 and every real number x > −1. If the exponent r is even, then the… …87

**Gibbs' inequality**— In information theory, Gibbs inequality is a statement about the mathematical entropy of a discrete probability distribution. Several other bounds on the entropy of probability distributions are derived from Gibbs inequality, including Fano s… …88

**Schur's inequality**— In mathematics, Schur s inequality, named after Issai Schur,establishes that for all non negative real numbers x , y , z and a positive number t ,:x^t (x y)(x z) + y^t (y z)(y x) + z^t (z x)(z y) ge 0with equality if and only if x = y = z or two… …89

**Poincaré inequality**— In mathematics, the Poincaré inequality is a result in the theory of Sobolev spaces, named after the French mathematician Henri Poincaré. The inequality allows one to obtain bounds on a function using bounds on its derivatives and the geometry of …90

**Bogomolov–Miyaoka–Yau inequality**— In mathematics, the Bogomolov–Miyaoka–Yau inequality is the inequality between Chern numbers of compact complex surfaces of general type. Its major interest is the way it restricts the possible topological types of the underlying real 4 manifold …91

**Noether inequality**— In mathematics, the Noether inequality, named after Max Noether, is a property of compact minimal complex surfaces that restricts the topological type of the underlying topological 4 manifold. It holds more generally for minimal projective… …92

**Sakurai's Bell inequality**— The intention of a Bell inequality is to serve as a test of local realism or local hidden variable theories as against quantum mechanics, applying Bell s theorem, which shows them to be incompatible. Not all the Bell s inequalities that appear in …93

**Rearrangement inequality**— In mathematics, the rearrangement inequality states that:x ny 1 + cdots + x 1y nle x {sigma (1)}y 1 + cdots + x {sigma (n)}y nle x 1y 1 + cdots + x ny nfor every choice of real numbers:x 1lecdotsle x nquad ext{and}quad y 1lecdotsle y nand every… …94

**Hoeffding's inequality**— Hoeffding s inequality, named after Wassily Hoeffding, is a result in probability theory that gives an upper bound on the probability for the sum of random variables to deviate from its expected value.Let :X 1, dots, X n ! be independent random… …95

**Vitale's random Brunn-Minkowski inequality**— In mathematics, Vitale s random Brunn Minkowski inequality is a theorem due to Richard Vitale that generalizes the classical Brunn Minkowski inequality for compact subsets of n dimensional Euclidean space R n to random compact sets.tatement of… …96

**Cauchy–Schwarz inequality**— In mathematics, the Cauchy–Schwarz inequality, also known as the Schwarz inequality, the Cauchy inequality, or the Cauchy–Schwarz–Bunyakovsky inequality, is a useful inequality encountered in many different settings, such as linear algebra… …97

**Law and Inequality**— Law and Inequality: A Journal of Theory and Practice , or the Journal of Law Inequality , is a journal of legal scholarship published by a student run group at University of Minnesota Law School. The journal is published twice a year, summer and… …98

**Carleman's inequality**— is an inequality in mathematics, named after Torsten Carleman. It states that if a 1, a 2, a 3, dots is a sequence of non negative real numbers, then : sum {n=1}^infty left(a 1 a 2 cdots a n ight)^{1/n} le e sum {n=1}^infty a n.The constant e in… …99

**MacLaurin's inequality**— In mathematics, MacLaurin s inequality, named after Colin Maclaurin, is a refinement of the inequality of arithmetic and geometric means. Let a 1, a 2, ..., a n be positive real numbers, and for k = 1, 2, ..., n define the averages S k as follows …100

**Milman's reverse Brunn-Minkowski inequality**— In mathematics, Milman s reverse Brunn Minkowski inequality is a result due to Vitali Milman that provides a reverse inequality to the famous Brunn Minkowski inequality for convex bodies in n dimensional Euclidean space R n . At first sight, such …