Closed subgroups generated by generic measure automorphisms

Abstract

We prove that for a generic measure preserving transformation $T$, the closed group generated by $T$ is a continuous homomorphic image of a closed linear subspace of $L_0(\lambda ,\mathbb{R})$, where $\lambda$ is Lebesgue measure, and that the closed group generated by $T$ contains an increasing sequence of finite dimensional toruses whose union is dense.

References in corpus (1)

• Generic representations of abelian groups and extreme amenability

Cited by in corpus (2)

• Generic properties of extensions
• Generic Behavior of a Measure Preserving Transformation