文摘
We study measures on compact spaces by analyzing the properties of fibers of continuous mappings into e358e33f3ed6f947ad48f03db8790" title="Click to view the MathML source">2ω. 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 e358e33f3ed6f947ad48f03db8790" title="Click to view the MathML source">2ω by a finite-to-one function is separable.