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

Alexander I. Bufetov (1)

1 I2M - Institut de Mathématiques de Marseille

The aim of this paper is to prove ergodic decomposition theo- rems for probability measures which are quasi-invariant under Borel actions of inductively compact groups as well as for σ-finite invariant measures. 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.

Domaines: Systèmes dynamiques [math.DS]; Théorie des groupes [math.GR]

Alexander I. Bufetov. Ergodic decomposition for measures quasi-invariant under a Borel action of an inductively compact group. Sbornik: Mathematics, 2014. ⟨hal-01256098⟩