Measures and fibers
Logic
2016-03-25 v1 General Topology
Abstract
We study measures on compact spaces by analyzing the properties of fibers of continuous mappings into 2^omega. We show that if a compact zerodimensional space K carries a measure of uncountable Maharam type, then such a mapping has a non-scattered fiber and, if we assume additionally a weak version of Martin's Axiom, such a mapping has a fiber carrying a measure of uncountable Maharam type. Also, we prove that every compact zerodimensional space which supports a strictly positive measure and which can be mapped into 2^omega by a finite-to-one function is separable.
Cite
@article{arxiv.1603.07501,
title = {Measures and fibers},
author = {Piotr Borodulin-Nadzieja},
journal= {arXiv preprint arXiv:1603.07501},
year = {2016}
}
Comments
17 pages