The measurable Hall theorem fails for treeings
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866909343363891200 |
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| author | Kun, Gábor |
| author_facet | Kun, Gábor |
| contents | We construct, for every $d \geq 3$, a $d$-regular acyclic measurably bipartite graphing that admits no measurable perfect matching, resolving a problem of Kechris and Marks.
A dense variant of our construction yields a coupling of two standard Borel probability measure spaces whose support contains no deterministic coupling, though the conditional probabilities of the coupling measure are atomless. This refutes a conjecture of Gurel-Gurevich and Peled. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_02013 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The measurable Hall theorem fails for treeings Kun, Gábor Combinatorics Dynamical Systems Logic 03E15, 05C21, 28D15 We construct, for every $d \geq 3$, a $d$-regular acyclic measurably bipartite graphing that admits no measurable perfect matching, resolving a problem of Kechris and Marks. A dense variant of our construction yields a coupling of two standard Borel probability measure spaces whose support contains no deterministic coupling, though the conditional probabilities of the coupling measure are atomless. This refutes a conjecture of Gurel-Gurevich and Peled. |
| title | The measurable Hall theorem fails for treeings |
| topic | Combinatorics Dynamical Systems Logic 03E15, 05C21, 28D15 |
| url | https://arxiv.org/abs/2106.02013 |