Ergodic Decomposition for Measures Quasi-Invariant Under Borel Actions of Inductively Compact Groups
arXiv:1105.0664
Abstract
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 sigma-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 the initial invariant measure (Theorem 2).
arXiv comment31 pages
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- Ergodic measures on compact metric spaces for isometric actions by inductively compact groups