Homogeneous probability measures on the Cantor set
arXiv:1812.09565 · doi:10.1016/j.jmaa.2019.07.041
Abstract
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.
arXiv commentSome corrections, new subsection added, final version (18 pages)