Ergodic and mixing probability measures on [SIN] groups (Q702406)

[SIN] denotes the class of locally compact groups which admit arbitrarily small conjugation-invariant neighbourhoods of the identity element. If \(G\) is a group of the class [SIN], then for any aperiodic probability measure, ergodicity and complete mixing are equivalent. The methods of the proof are relied on certain deep properties of boundaries of the associated random walks. In particular, every compactly generated totally disconnected nilpotent locally compact group is [SIN] and then every adapted probability on such a group is ergodic.