A characterization of the relative entropies

TL;DR

This paper characterizes a family of relative entropies parameterized by alpha, based on recursivity and symmetry, with minimal regularity assumptions for most cases, advancing theoretical understanding of entropy measures.

Contribution

It provides a new characterization of relative entropies depending on a real parameter alpha, with minimal assumptions, extending previous results.

Findings

Characterization of relative entropies for different alpha values

Minimal regularity assumptions for most cases

Special cases for alpha=0 and alpha=1 with additional assumptions

Abstract

In this note we give a characterization of a family of relative entropies on open domain depending on a real parameter $\alpha$ based on recursivity and symmetry. In the cases $\alpha=1$ and $\alpha=0$ we use additionally a weak regularity assumption while in the other cases no regularity assumptions are made at all.