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On a property of the Legendre transform

A. A. Mogul'skiĭ<sup>ab

a</sup> Sobolev Institute of Mathematics, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Abstract: For a pair of convex lower semicontinuous functions connected by the Legendre transform, we establish that their derivatives are mutually inverse functions (in the generalized sense).

Key words: deviation rate function, logarithm of the Laplace transform, Legendre transform, generalized inverse function.

UDC: 519.21

Received: 03.05.2016

DOI: 10.17377/mattrudy.2017.20.109

 English version: Siberian Advances in Mathematics, 2018, 28:1, 65–73

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