Prelude: a user’s guide to convexity

  • Jean-François Collet
Part of the Universitext book series (UTX)


This chapter could be called a primer on convexity for probabilists, since it brings together some of the theory of convex functions with a view toward applications to information theory. In particular, a certain number of classical convexity inequalities (such as Jensen’s and Young’s inequalities) are presented in a unified framework thanks to the use of Bregman’s divergences.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire J.A. DieudonnéUniversité de Nice Sophia-AntipolisNice Cedex 02France

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