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arXiv · 1108.0625

Uniform sets for infinite measure-preserving systems

Hisatoshi Yuasa
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Abstract

The concept of a uniform set is introduced for an ergodic, measure-preserving transformation on a non-atomic, infinite Lebesgue space. The uniform sets exist as much as they generate the underlying $σ$-algebra. This leads to the result that any ergodic, measure-preserving transformation on a non-atomic, infinite Lebesgue space is isomorphic to a minimal homeomorphism on a locally compact metric space which admits a unique, up to scaling, invariant Radon measure.

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Hisatoshi Yuasa. 2011-08-19. Uniform sets for infinite measure-preserving systems. https://arxiv.org/abs/1108.0625

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