Kudō-continuity of conditional entropies
Artikel i vetenskaplig tidskrift, 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.
Non-monotone sequences of σ-algebras
Conditional entropy
Författare
Michael Björklund
Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori
Yair Hartman
Ben-Gurion University of the Negev
Hanna Oppelmayer
University of Innsbruck
Annales de linstitut Henri Poincare (B) Probability and Statistics
0246-0203 (ISSN)
Vol. 59 3 1677-1687Ämneskategorier
Matematik
Matematisk analys
DOI
10.1214/22-AIHP1313