Measures and fibers

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• 作者：Piotr Borodulin-Nadzieja¹ ; ^{pborod@math.uni.wroc.pl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：03E35 ; 03E75 ; 28A60
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：1 September 2016
• 年：2016
• 卷：210
• 期：Complete
• 页码：201-215
• 全文大小：414 K

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">2^ω$2^{\omega }$. 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 e358e33f3ed6f947ad48f03db8790" title="Click to view the MathML source">2^ω$2^{\omega }$ by a finite-to-one function is separable.