Homogeneous probability measures on the Cantor set

Homogeneous probability measures on the Cantor set

We show that every homeomorphism between closed measure zero subsets extends to a measure preserving auto-homeomorphism, whenever the Cantor set is endowed with a suitable probability measure. This is valid both for the standard product measure, as well as for the universal homogeneous rational meas...

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Veröffentlicht in:arXiv.org 2019-07
Hauptverfasser: Bielas, W, Kubiś, W, Walczyńska, M
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - General Topology
Mathematics - Probability
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Zusammenfassung:We show that every homeomorphism between closed measure zero subsets extends to a measure preserving auto-homeomorphism, whenever the Cantor set is endowed with a suitable probability measure. This is valid both for the standard product measure, as well as for the universal homogeneous rational measure.
ISSN:2331-8422
DOI:10.48550/arxiv.1812.09565