KudoContinuity Of Entropy Functionals
Abstract
We study in this paper realvalued functions on the space of all sub$\sigma$algebras of a probability measure space, and introduce the notion of Kudocontinuity, which is an a priori strengthening of continuity with respect to strong convergence. We show that a large class of entropy functionals are Kudocontinuous. 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2020
 DOI:
 10.48550/arXiv.2002.06647
 arXiv:
 arXiv:2002.06647
 Bibcode:
 2020arXiv200206647B
 Keywords:

 Mathematics  Probability;
 Mathematics  Dynamical Systems
 EPrint:
 32 pages