Jensen's inequality
In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proven by Jensen in 1906. Given its generality, the inequality appears in many forms depending on the context, some of which are presented below. In its simplest form the inequality states that the convex transformation of a mean is less than or equal to the mean applied after convex transformation; it is a simple corollary that the opposite is true of concave transformations. Thus, Jensen's inequality is
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Jensen's inequality
In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proven by Jensen in 1906. Given its generality, the inequality appears in many forms depending on the context, some of which are presented below. In its simplest form the inequality states that the convex transformation of a mean is less than or equal to the mean applied after convex transformation; it is a simple corollary that the opposite is true of concave transformations. Thus, Jensen's inequality is
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A desigualdade de Jensen, devi ...... (podendo E(X2) ser infinito).
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De ongelijkheid van Jensen is ...... reële as is (a=–∞ en/of b=+∞).
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Die jensensche Ungleichung ist ...... m Mittel dieser n Stellen ist.
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En matemáticas, la desigualdad ...... parece en múltiples contextos.
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En mathématiques, et plus préc ...... me, très utilisée en physique.
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In mathematics, Jensen's inequ ...... d φ is a convex function, then
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La disuguaglianza di Jensen (d ...... i sono presentati nel seguito.
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Nierówność Jensena – nierównoś ...... skiego matematyka i inżyniera.
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Нера́венство Йе́нсена — нераве ...... определением выпуклой функции.
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متراجحة ينسن في الرياضيات، وال ...... المحدب لنفس المتغير أو القيم".
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Jensen inequality
Jensen's inequality
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JensensInequality
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A desigualdade de Jensen, devi ...... (podendo E(X2) ser infinito).
@pt
De ongelijkheid van Jensen is ...... reële as is (a=–∞ en/of b=+∞).
@nl
Die jensensche Ungleichung ist ...... bereits 1889 bei Otto Hölder.
@de
En matemáticas, la desigualdad ...... parece en múltiples contextos.
@es
En mathématiques, et plus préc ...... om d'inégalité de Gibbs (en)).
@fr
In mathematics, Jensen's inequ ...... . Thus, Jensen's inequality is
@en
La disuguaglianza di Jensen (d ...... i sono presentati nel seguito.
@it
Nierówność Jensena – nierównoś ...... skiego matematyka i inżyniera.
@pl
Нера́венство Йе́нсена — нераве ...... определением выпуклой функции.
@ru
متراجحة ينسن في الرياضيات، وال ...... المحدب لنفس المتغير أو القيم".
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label
Desigualdad de Jensen
@es
Desigualdade de Jensen
@pt
Disuguaglianza di Jensen
@it
Inégalité de Jensen
@fr
Jensen's inequality
@en
Jensensche Ungleichung
@de
Nierówność Jensena
@pl
Ongelijkheid van Jensen
@nl
Неравенство Йенсена
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متباينة ينسن
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