A generic transformation is invertible
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909023141363712 |
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| author | Eisner, Tanja |
| author_facet | Eisner, Tanja |
| contents | We show that, on a standard non-atomic probability space, invertible measure-preserving transformations form a dense $G_δ$ subset of the space of all measure-preserving transformations endowed with the strong (=weak) operator topology. This implies that all properties which are generic for invertible transformations are also generic for general ones. We further show that invertible Koopman operators form a dense $G_δ$ subset of all bi-stochastic operators for the weak operator topology, and the same holds for general Koopman operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19893 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A generic transformation is invertible Eisner, Tanja Dynamical Systems Functional Analysis We show that, on a standard non-atomic probability space, invertible measure-preserving transformations form a dense $G_δ$ subset of the space of all measure-preserving transformations endowed with the strong (=weak) operator topology. This implies that all properties which are generic for invertible transformations are also generic for general ones. We further show that invertible Koopman operators form a dense $G_δ$ subset of all bi-stochastic operators for the weak operator topology, and the same holds for general Koopman operators. |
| title | A generic transformation is invertible |
| topic | Dynamical Systems Functional Analysis |
| url | https://arxiv.org/abs/2512.19893 |