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Representation formula for the entropy and functional inequalities

Joseph Lehec (2013)

Annales de l'I.H.P. Probabilités et statistiques

We prove a stochastic formula for the Gaussian relative entropy in the spirit of Borell’s formula for the Laplace transform. As an application, we give simple proofs of a number of functional inequalities.

Representation of continuous associative functions.

Barbara Baccheli (1986)

Stochastica

Strengthened forms of Ling's representation theorem concerning a class of continuous associative functions are given: Firstly the monotonicity condition is removed. Then the associativity condition is replaced by the power associativity.

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