Entropy Theory for Cross Sections

Abstract

We define the notion of entropy for a cross section of an action of continuous amenable group and relate it to the entropy of the ambient action. As a result, we are able to answer a question of J.P. Thouvenot about completely positive entropy actions.

arXiv comment26 pages; v2 Main result is stated for groups with zero self-entropy, 34 pages; v3 final version. To be published at GAFA