Separating topological recurrence from measurable recurrence: exposition and extension of Kriz's example
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866910762538106880 |
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| author | Griesmer, John T. |
| author_facet | Griesmer, John T. |
| contents | We prove that for every infinite set $E\subset \mathbb Z$, there is a set $S\subset E-E$ which is a set of topological recurrence and not a set of measurable recurrence. This extends a result of Igor Kriz, proving that there is a set of topological recurrence which is not a set of measurable recurrence. Our construction follows Kriz's closely, and this paper can be considered an exposition of the original argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_01642 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Separating topological recurrence from measurable recurrence: exposition and extension of Kriz's example Griesmer, John T. Dynamical Systems Combinatorics 11B30 We prove that for every infinite set $E\subset \mathbb Z$, there is a set $S\subset E-E$ which is a set of topological recurrence and not a set of measurable recurrence. This extends a result of Igor Kriz, proving that there is a set of topological recurrence which is not a set of measurable recurrence. Our construction follows Kriz's closely, and this paper can be considered an exposition of the original argument. |
| title | Separating topological recurrence from measurable recurrence: exposition and extension of Kriz's example |
| topic | Dynamical Systems Combinatorics 11B30 |
| url | https://arxiv.org/abs/2108.01642 |