Kudō-continuity条件熵

IF 1.5 Q2 PHYSICS, MATHEMATICAL Annales de l Institut Henri Poincare D Pub Date : 2023-08-01 DOI:10.1214/22-aihp1313

M. Björklund, Yair Hartman, Hanna Oppelmayer

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摘要

．本文引入了标准概率空间中所有完备子- σ -代数空间上实值函数的kuo -连续性的概念。这是对强收敛性的连续性的先验强化。我们证明了条件熵是kudo连续的，并讨论了在SAT*-空间的Furstenberg熵谱研究中的应用。

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Kudō-continuity of conditional entropies

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

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