Complete nonmeasurability in regular families

Details Complete nonmeasurability in regular families Complete nonmeasurability in regular families

2010-09-06

arxiv.org/abs/1009.1022v1

Houston Journal of Mathematics, 34 (3) (2008), pp. 773-780

Mathematics

Logic

7 pages

Scientific paper

We show that for a $\sigma $-ideal $\ci$ with a Borel base of subsets of an uncountable Polish space, if $\ca$ is (in several senses) a "regular" family of subsets from $\ci $ then there is a subfamily of $\ca$ whose union is completely nonmeasurable i.e. its intersection with every Borel set not in $\ci $ does not belong to the smallest $\sigma $-algebra containing all Borel sets and $\ci.$ Our results generalize results from \cite{fourpoles} and \cite{fivepoles}.

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