论文标题
熵功能的Kudo-continition
Kudo-Continuity Of Entropy Functionals
论文作者
论文摘要
我们在本文中研究了概率测量空间的所有亚$σ$ - 代数的空间的实价函数，并引入了kudo-continition的概念，这是对强收敛的先验增强连续性的概念。我们表明，大量的熵功能是kudo的连续功能。在途中，我们建立了各种熵函数相对于渐近二阶随机统治的上层和下连续性，这应该具有独立的关注。给出了与本地紧凑型组随机步行相关的$μ$ bungaries的熵光谱的应用。
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.
