Kudō-continuity of conditional entropies

Michael Björklund, Yair Hartman, Hanna Oppelmayer

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)1677-1687
Number of pages11
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume59
Issue number3
DOIs
StatePublished - Aug 2023

Keywords

  • Conditional entropy
  • Non-monotone sequences of σ-algebras

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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