TY - UNPB
T1 - Kudo-Continuity Of Entropy Functionals
AU - Björklund, Michael
AU - Hartman, Yair
AU - Oppelmayer, Hanna
PY - 2020/2/16
Y1 - 2020/2/16
N2 - 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.
AB - 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.
KW - Mathematics - Probability
KW - Mathematics - Dynamical Systems
U2 - 10.48550/arXiv.2002.06647
DO - 10.48550/arXiv.2002.06647
M3 - Preprint
BT - Kudo-Continuity Of Entropy Functionals
ER -