# inequality

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**Entropy power inequality**— In mathematics, the entropy power inequality is a result in probability theory that relates to so called entropy power of random variables. It shows that the entropy power of suitably well behaved random variables is a superadditive function. The …142

**Remez inequality**— In mathematics the Remez inequality, discovered by the Ukrainian mathematician E. J. Remez in 1936, gives a bound on the sup norms of certain polynomials, the bound being attained by the Chebyshev polynomials.The inequalityLet sigma; be an… …143

**Gromov's inequality**— The following pages deal with inequalities due to Mikhail Gromov:see Bishop Gromov inequalitysee Gromov s inequality for complex projective spacesee Gromov s systolic inequality for essential manifoldssee Lévy Gromov inequality …144

**Mahler's inequality**— In mathematics, Mahler s inequality states that the geometric mean of the term by term sum of two finite sequences of positive numbers is greater than or equal to the sum of their two separate geometric means: when xk, yk > 0 for all k. The… …145

**Marcinkiewicz–Zygmund inequality**— In mathematics, the Marcinkiewicz–Zygmund inequality, named after Józef Marcinkiewicz and Antoni Zygmund, gives relations between moments of a collection of independent random variables. It is a generalization of the rule for the sum of variances …146

**Vysochanskiï-Petunin inequality**— In probability theory, the Vysochanskij Petunin inequality gives a lower bound for the probability that a random variable with finite variance lies within a certain number of standard deviations of the variable s mean, or equivalently an upper… …147

**Rushbrooke inequality**— In statistical mechanics, the Rushbrooke inequality relates the critical exponents of a magnetic system which exhibits a first order phase transition in the thermodynamic limit for non zero temperature T .Since the Helmholtz free energy is… …148

**Linear matrix inequality**— In convex optimization, a linear matrix inequality (LMI) is an expression of the form: LMI(y):=A 0+y 1A 1+y 2A 2+cdots+y m A mgeq0,where * y= [y i,, i!=!1dots m] is a real vector, * A 0,, A 1,, A 2,,dots,A m are symmetric matrices in the subspace …149

**Friedrichs' inequality**— In mathematics, Friedrichs inequality is a theorem of functional analysis, due to Kurt Friedrichs. It places a bound on the Lp norm of a function using Lp bounds on the weak derivatives of the function and the geometry of the domain, and can be… …150

**Landau-Kolmogorov inequality**— In mathematics, the Landau Kolmogorov inequality is an inequality between different derivatives of a function. There are many inequalities holding this name (sometimes they are also called Kolmogorov type inequalities), common formula is:… …151

**Jackson's inequality**— In approximation theory, Jackson s inequality is an inequality (proved by Dunham Jackson) between the value of function s best approximation by polynomials and the modulus of continuity of its derivatives. Here is one of the simple cases… …152

**Eilenberg's inequality**— is a mathematical inequality for Lipschitz continuous functions.Let f : X rarr; Y be a Lipschitz continuous function between separable metric spaces whose Lipschitz constant is denoted by Lip f . Then, Eilenberg s inequality states that:int Y^* H …153

**Khintchine inequality**— In mathematics, the Khintchine inequality, named after Aleksandr Khinchin and spelled in multiple ways in the Roman alphabet, is a theorem from probability, and is also frequently used in analysis. Heuristically, it says that if we pick N complex …154

**Wirtinger inequality (2-forms)**— For other inequalities named after Wirtinger, see Wirtinger s inequality. In mathematics, the Wirtinger inequality for 2 forms, named after Wilhelm Wirtinger, states that the exterior scriptstyle uth power of the standard symplectic form omega;,… …155

**Wirtinger's inequality**— is either of two inequalities named after Wilhelm Wirtinger:* Wirtinger s inequality for functions * Wirtinger inequality (2 forms) …156

**Fisher's inequality**— In combinatorial mathematics, Fisher s inequality, named after Ronald Fisher, is a necessary condition for the existence of a balanced incomplete block design satisfying certain prescribed conditions.Fisher, a population geneticist and… …157

**Von Neumann's inequality**— In operator theory, von Neumann s inequality, due to John von Neumann, states that, for a contraction T acting on a Hilbert space and a polynomial p , then the norm of p ( T ) is bounded by the supremum of | p ( z )| for z in the unit disk. [… …158

**Multidimensional Chebyshev's inequality**— In probability theory, the multidimensional Chebyshev s inequality is a generalization of Chebyshev s inequality, which puts a bound on the probability of the event that a random variable differs from its expected value by more than a specified… …159

**Bishop–Gromov inequality**— In mathematics, the Bishop–Gromov inequality is a classical theorem in Riemannian geometry, named after Richard L. Bishop and Mikhail Gromov. It is the key point in the proof of Gromov s compactness theorem.tatementLet us denote by S^m k a… …160

**Peetre's inequality**— In mathematics, Peetre s inequality says that for any real number t and any vectors x and y in Rn, the following inequality holds:: left( frac{1+|x|^2}{1+|y|^2} ight)^t le 2^ (1+|x y|^2)^.References …