# inequality

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**Hadwiger–Finsler inequality**— In mathematics, the Hadwiger–Finsler inequality is a result on the geometry of triangles in the Euclidean plane, named after the mathematicians Hugo Hadwiger and Paul Finsler. It states that if a triangle in the plane has side lengths a , b and c …122

**Erdős–Mordell inequality**— In geometry, the Erdős–Mordell inequality states that for any triangle ABC and point O inside ABC , the sum of the distances from O to the sides is less than or equal to half of the sum of the distances from O to the vertices. The inequality was… …123

**Racial inequality in the American criminal justice system**— Race Inequalities in the Criminal Justice System is a topic that has become increasingly more relative with the rising penal population in the United States. Education and race seem to be the most decisive factors when deciding who goes to jail… …124

**Correlation inequality**— In probability and statistics, a correlation inequality is one of a number of inequalities satisfied by the correlation functions of a model. Such inequalities are of particular use in statistical mechanics and in percolation theory. Examples… …125

**Chebyshev's sum inequality**— For the similarly named inequality in probability theory, see Chebyshev s inequality. In mathematics, Chebyshev s sum inequality, named after Pafnuty Chebyshev, states that if and then Similarly, if …126

**Variational inequality**— is a mathematical theory intended for the study of equilibrium problems. Guido Stampacchia put forth the theory in 1964 to study partial differential equations. The applicability of the theory has since been expanded to include problems from… …127

**Shapiro inequality**— In mathematics, the Shapiro inequality is an inequality due to H. Shapiro and Vladimir Drinfel d.tatement of the inequalitySuppose n is a natural number and x 1, x 2, dots, x n are positive numbers and:* n is even and less than or equal to 12, or …128

**Hardy's inequality**— is an inequality in mathematics, named after G. H. Hardy. It states that if a 1, a 2, a 3, dots is a sequence of non negative real numbers which is not identically zero, then for every real number p > 1 one has:sum {n=1}^infty left (frac{a 1+a… …129

**Markov brothers' inequality**— In mathematics, the Markov brothers inequality is an inequality proved by Andrey Markov and Vladimir Markov. This inequality bounds the maximum of the derivatives of a polynomial on an interval in terms of the maximum of the polynomial.[1] For k …130

**Paley–Zygmund inequality**— In mathematics, the Paley Zygmund inequality bounds theprobability that a positive random variable is small, in terms ofits mean and variance (i.e., its first two moments). The inequality wasproved by Raymond Paley and Antoni Zygmund.Theorem: If… …131

**Ono's inequality**— In mathematics, Ono s inequality is a theorem about triangles in the Euclidean plane. In its original form, as conjectured by T. Ono in 1914, the inequality is actually false; however, the statement is true for acute triangles, as shown by… …132

**Korn's inequality**— In mathematics, Korn s inequality is a result about the derivatives of Sobolev functions. Korn s inequality plays an important rôle in linear elasticity theory.tatement of the inequalityLet Omega; be an open, connected domain in n dimensional… …133

**Hermite–Hadamard inequality**— dablink|Another inequality is called Hadamard s inequality.In mathematics, the Hermite–Hadarmard inequality, named after Charles Hermite and Jacques Hadamard and sometimes also called Hadamard s inequality, states that if a function fnof; : [ a …134

**Wigner-d'Espagnat inequality**— The Wigner d Espagnat inequality is a basic result of set theory.It is named for Eugene Wigner and Bernard d Espagnat who (as pointed out by Bell) both employed it in their popularizations of quantum mechanics.Given a set S with three subsets, J …135

**Boole's inequality**— In probability theory, Boole s inequality, named after George Boole, (also known as the union bound) says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the… …136

**An Essay on the Inequality of the Human Races**— (1853 ndash;1855) by Joseph Arthur Comte de Gobineau is a voluminous work; while originally intended as a work of philosophical enquiry, it is today considered as one of the earliest examples of scientific racism. Expanding upon Boulainvilliers… …137

**Harnack's inequality**— In mathematics, Harnack s inequality is an inequality relating the values of a positive harmonic function at two points, introduced by *Citation | last1=Hamilton | first1=Richard S. | title=The Harnack estimate for the Ricci flow | id=MathSciNet… …138

**Fano's inequality**— In information theory, Fano s inequality (also known as the Fano converse and the Fano lemma) relates the average information lost in a noisy channel to the probability of the categorization error. It was derived by Robert Fano in the early 1950s …139

**Levinson's inequality**— In mathematics the Levinson s inequality is the following inequality involving positive numbers: Let a>0 and f be a given function having a third derivative on the range ] 0,2a [, and such that :f (x)geq 0 for all xin ] 0,2a [. If 0 …140

**McDiarmid's inequality**— McDiarmid s inequality, named after Colin McDiarmid, is a result in probability theory that gives an upper bound on the probability for the value of a function depending on multiple independent random variables to deviate from its expected value …