Ergodic decomposition of quasi-invariant probability measures

Ergodic decomposition for measures quasi-invariant under a Borel action of an inductively compact group

The aim of this paper is to prove ergodic decomposition theorems for probability measures quasi-invariant under Borel actions of inductively compact groups (Theorem 1) as well as for σ-finite invariant measures (Corollary 1). For infinite measures the ergodic decomposition is not unique, but the measure class of the decomposing measure on the space of projective measures is uniquely defined by ...

Conditionally Invariant Probability Measures

V eronique Maume-Deschamps Section de Math ematiques, Universit e de Gen eve 2-4 rue du Lievre CP 240 Suisse. Abstract Let T be a measurable map on a Polish space X, let Y be a non trivial subset of X. We give conditions ensuring existence of conditionally invariant probability measures (to non absorption in Y). We also supply suucient conditions for these probability measures to be absolutely ...

On the space of ergodic invariant measures of unipotent flows

Let G be a Lie group and Γ be a discrete subgroup. We show that if {μn} is a convergent sequence of probability measures on G/Γ which are invariant and ergodic under actions of unipotent one-parameter subgroups, then the limit μ of such a sequence is supported on a closed orbit of the subgroup preserving it, and is invariant and ergodic for the action of a unipotent one-parameter subgroup of G.

Existence of Bounded Invariant Measures in Ergodic Theory

Ergodic sequences of probability measures on commutative hypergroups

We study conditions on a sequence of probability measures {µ n } n on a commutative hyper-group K, which ensure that, for any representation π of K on a Hilbert space Ᏼ π and for any ξ ∈ Ᏼ π , (K π x (ξ)dµ n (x)) n converges to a π-invariant member of Ᏼ π. 1. Introduction. The mean ergodic theorem was originally formulated by von Neu-mann [13] for one-parameter unitary groups in Hilbert space. ...