Abstract
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.
Original language | English |
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Pages (from-to) | 1677-1687 |
Number of pages | 11 |
Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |
Volume | 59 |
Issue number | 3 |
DOIs | |
State | Published - 1 Jan 2023 |
Keywords
- Conditional entropy
- Non-monotone sequences of σ-algebras
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty