Kudō-continuity of conditional entropies

Michael Björklund; Yair Hartman; Hanna Oppelmayer

doi:10.1214/22-AIHP1313

Kudō-continuity of conditional entropies

Michael Björklund, Yair Hartman, Hanna Oppelmayer

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-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 language	American English
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	https://doi.org/10.1214/22-AIHP1313
State	Published - 1 Jan 2023

Keywords

Conditional entropy
Non-monotone sequences of σ-algebras

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/22-AIHP1313

Cite this

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ER -

Kudō-continuity of conditional entropies

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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