# inequality

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**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 Rn. At first sight, such a …102

**Azuma's inequality**— In probability theory, the Azuma Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) gives a concentration result for the values of martingales that have bounded differences.Suppose { X k : k = 0, 1, 2, 3, ... } is a martingale …103

**An inequality on location and scale parameters**— For probability distributions having an expected value and a median, the mean (i.e., the expected value) and the median can never differ from each other by more than one standard deviation. To express this in mathematical notation, let mu; , m ,… …104

**Weyl's inequality**— In mathematics, there are at least two results known as Weyl s inequality .Weyl s inequality in number theoryIn number theory, Weyl s inequality, named for Hermann Weyl, states that if M , N , a and q are integers, with a and q coprime, q > 0,… …105

**Differential variational inequality**— In mathematics, a differential variational inequality (DVI) is a dynamical system that incorporates ordinary differential equations and variational inequalities or complementarity problems. DVIs are useful for representing models involving both… …106

**Etemadi's inequality**— In probability theory, Etemadi s inequality is a so called maximal inequality , an 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… …107

**Karamata's inequality**— In mathematics, Karamata s inequality, also known as the Majorization Inequality, states that if f(x) is a convex function in x and the sequence :x 1, x 2, ..., x n majorizes:y 1, y 2, ..., y n then :f(x 1)+f(x 2)+...+f(x n) ge f(y 1)+f(y… …108

**Borell-Brascamp-Lieb inequality**— In mathematics, the Borell Brascamp Lieb inequality is an integral inequality due to many different mathematicians but named after Christer Borell, Herm Jan Brascamp and Elliott Lieb.The result was proved for p gt; 0 by Henstock and Macbeath in… …109

**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 …110

**Riemannian Penrose inequality**— In mathematical general relativity, the Penrose inequality, first conjectured by Sir Roger Penrose, estimates the mass of a spacetime in terms of the total area of its black holes and is a generalization of the positive mass theorem. The… …111

**Linear inequality**— In mathematics a linear inequality is an inequality which involves a linear function.Formal definitionsWhen operating in terms of real numbers, linear inequalities are the ones written in the forms: f(x) < b ext{ or }f(x) leq b,where f(x) is a… …112

**Chebyshev's inequality**— ▪ mathematics also called Bienaymé Chebyshev inequality in probability theory, a theorem that characterizes the dispersion of data away from its mean (average). The general theorem is attributed to the 19th century Russian mathematician… …113

**Pedoe's inequality**— In geometry, Pedoe s inequality, named after Daniel Pedoe, states that if a , b , and c are the lengths of the sides of a triangle with area f , and A , B , and C are the lengths of the sides of a triangle with area F , then:A^2(b^2+c^2… …114

**Lubell-Yamamoto-Meshalkin inequality**— In combinatorial mathematics, the Lubell Yamamoto Meshalkin inequality, more commonly known as the LYM inequality, is an inequality on the sizes of sets in a Sperner family, proved by harvtxt|Bollobás|1965, harvtxt|Lubell|1966,… …115

**Bernstein's inequality (mathematical analysis)**— In the mathematical theory of mathematical analysis, Bernstein s inequality, named after Sergei Natanovich Bernstein, is defined as follows.Let P be a polynomial of degree n with derivative P prime; . Then:max(P ) le ncdotmax(P) where we define… …116

**Bessel's inequality**— In mathematics, especially functional analysis, Bessel s inequality is a statement about the coefficients of an element x in a Hilbert space with respect to an orthonormal sequence.Let H be a Hilbert space, and suppose that e 1, e 2, ... is an… …117

**Gårding's inequality**— In mathematics, Gårding s inequality is a result that gives a lower bound for the bilinear form induced by a real linear elliptic partial differential operator. The inequality is named after Lars Gårding.tatement of the inequalityLet Omega; be a… …118

**Dvoretzky–Kiefer–Wolfowitz inequality**— In the theory of probability and statistics, the Dvoretzky–Kiefer–Wolfowitz inequality predicts how close an empirically determined distribution function will be to the distribution function from which the empirical samples are drawn. It is named …119

**Kolgomorov's inequality**— Kolmogorov s inequality is an inequality which gives a relation among a function and its first and second derivatives. Kolmogorov s inequality states the following:Let f colon mathbb{R} ightarrow mathbb{R} be a twice differentiable function on… …120

**Bonnesen's inequality**— is an 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 isoperimetric inequality.More precisely, consider a planar simple closed curve …