Kudō-continuity of conditional entropies

Journal article, 2023

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