Recurrence and the existence of invariant measures
| Autor: | Manuel J. Inselmann, Benjamin D. Miller |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Logic Group (mathematics) 010102 general mathematics Mathematics::General Topology Dynamical Systems (math.DS) Mathematics - Logic Space (mathematics) 01 natural sciences Philosophy Mathematics::Logic 0103 physical sciences FOS: Mathematics 03E15 28A05 (Primary) 010307 mathematical physics Invariant measure Locally compact space 0101 mathematics Orbit (control theory) Invariant (mathematics) Mathematics - Dynamical Systems Borel set Logic (math.LO) Probability measure Mathematics |
| Popis: | We show that recurrence conditions do not yield invariant Borel probability measures in the descriptive set-theoretic milieu, in the strong sense that if a Borel action of a locally compact Polish group on a standard Borel space satisfies such a condition but does not have an orbit supporting an invariant Borel probability measure, then there is an invariant Borel set on which the action satisfies the condition but does not have an invariant Borel probability measure. To appear in the Journal of Symbolic Logic |
| Databáze: | OpenAIRE |
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