熵泛函的Kudo连续性
Kudo-Continuity Of Entropy Functionals
摘要：
本文研究了概率测度空间的所有子$σ$ -代数构成的空间上的实值函数，并引入了Kudo-连续性的概念，它是连续性在强收敛性方面的先验加强.我们证明了一大类熵泛函是Kudo连续的。在此基础上，我们建立了各种熵函数关于渐近二阶随机控制的上、下连续性，这应该是我们独立感兴趣的。给出了在局部紧群上随机游动的$μ$ -边界熵谱研究中的一个应用。
英文摘要：
We study in this paper real-valued functions on the space of all sub-$σ$-algebras of a probability measure space, and introduce the notion of Kudo-continuity, which is an a priori strengthening of continuity with respect to strong convergence. We show that a large class of entropy functionals are Kudo-continuous. On the way, we establish upper and lower continuity of various entropy functions with respect to asymptotic second order stochastic domination, which should be of independent interest. An application to the study of entropy spectra of $μ$-boundaries associated to random walks on locally compact groups is given.
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