Kudo-Continuity Of Entropy Functionals

Michael Björklund, Yair Hartman, Hanna Oppelmayer

Publikation: Beitrag in einer FachzeitschriftArtikel

Abstract

We study in this paper real-valued functions on the space of all sub-$\sigma$-algebras of a probability measure space, and introduce the notion of Kudo-continuity, which is an a priori strengthening of continuity with respect to strong convergence. We show that a large class of entropy functionals are Kudo-continuous. On the way, we establish upper and lower continuity of various entropy functions with respect to asymptotic second order stochastic domination, which should be of independent interest. An application to the study of entropy spectra of $\mu$-boundaries associated to random walks on locally compact groups is given.
Originalspracheenglisch
FachzeitschriftAnnales Henri Poincaré
PublikationsstatusEingereicht - 2020

Fingerprint Untersuchen Sie die Forschungsthemen von „Kudo-Continuity Of Entropy Functionals“. Zusammen bilden sie einen einzigartigen Fingerprint.

Dieses zitieren