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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 proved by Jensen in 1906, building on an earlier proof of the same inequality for doubly-differentiable functions by Otto Hölder in 1889. Given its generality, the…

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Jensen's inequality

Nodes60
Edges59
Triples75
Avg. degree1.97
Density0.033333
Components1

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Jensen's inequality

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related to References · 31
Jensen's inequality → American Mathematical Monthly, Analisi Matematica Due, Averages, Cambridge University Press, Carlo Sbordone, Complex Analysis, David Chandler, Dec, Examples, Face, Introduction, ISBN, Liguori, McGraw-Hill, Modern Statistical Mechanics, Nicola Fusco, Oxford, Paolo Marcellini, Probability, Real
related to External links · 16
Jensen's inequality → Arthur Lohwater, EMS Press, Encyclopedia, Eric, Hansen, Inequalities, Introduction, Jensen, Jensen's, Jensen's Operator Inequality, Mathematics, MathWorld, Online, PDF, Pedersen, Weisstein
related to Intuitive graphical proof · 7
Jensen's inequality → Assuming, Before, Consequently, Jensen's, Noticing, This, X0
related to Generalizations · 5
Jensen's inequality → Beyond, Hansen, In, Jensen's, Pedersen
related to Information theory · 3
Jensen's inequality → If, Jensen's, Therefore
related to Rao–Blackwell theorem · 3
Jensen's inequality → If, Jensen's, So
related to Statements · 3
Jensen's inequality → In, Jensen's, The
related to Finite form · 2
Jensen's inequality → For, Jensen's
related to Risk aversion · 2
Jensen's inequality → Jensen's, The
see also · 2
Jensen's inequality → Jensen's, Karamata's

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inequality displaystyle convex function jensen's varphi probability variable real form random operatorname jensen general theory one statement case finite measure

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SubjectPredicateObjectConfidenceSrc
Jensen's inequalityrelated to External linksJensen's Operator Inequality0.60section
Jensen's inequalityrelated to External linksHansen0.60section
Jensen's inequalityrelated to External linksPedersen0.60section
Jensen's inequalityrelated to External linksJensen0.60section
Jensen's inequalityrelated to External linksEncyclopedia0.60section
Jensen's inequalityrelated to External linksMathematics0.60section
Jensen's inequalityrelated to External linksEMS Press0.60section
Jensen's inequalityrelated to External linksWeisstein0.60section
Jensen's inequalityrelated to External linksEric0.60section
Jensen's inequalityrelated to External linksJensen's0.60section
Jensen's inequalityrelated to External linksMathWorld0.60section
Jensen's inequalityrelated to External linksArthur Lohwater0.60section

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