Mariusz Lema´nczyk
Entropy of Gaussian Actions for Countable Abelian Groups
The paper is published: Fund. Math. 157, No. 2-3 (1998) 277-286

MSC:

28D05 Measure-preserving transformations

Abstract: We prove that for any countable Abelian group $A$ and any its Gaussian
action, the entropy is either zero or infinity and moreover, the former
case happens iff the spectral measure of the Gaussian action is singular
with respect to Haar measure on the dual of $A$.