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.
Some corrections, new subsection added, final version (18 pages)