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Basic objects of ergodic theory are invariant measures, measure-preserving transformations/systems and the corresponding Koopman operators, which will be introduced in this chapter. We present basic results and discuss various examples showing connections to other areas such as group theory, probability theory, number theory and topology.

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Measure-Preserving Systems

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  • 发表日期：

    2025年

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  • Tanja Eisner,
  • Bálint Farkas

摘要

Basic objects of ergodic theory are invariant measures, measure-preserving transformations/systems and the corresponding Koopman operators, which will be introduced in this chapter. We present basic results and discuss various examples showing connections to other areas such as group theory, probability theory, number theory and topology.