Kudō-continuity of conditional entropies

Abstract

. In this paper we introduce the notion of Kudo-continuity for real-valued functions on the space of all complete sub- σ -algebras of a standard probability space. This is an a priori strengthening of continuity with respect to strong convergence. We show that conditional entropies are Kudo-continuous, and discuss an application to the study of Furstenberg entropy spectra of SAT*-spaces.