Remarks on nonmeasurable unions of big point families

Abstract

We show that under some conditions on a family $\mathcal{A}\subset\bbi$ there exists a subfamily ${\mathcal{A}}_0\subset \mathcal{A}$ such that $\bigcup {\mathcal{A}}_0$ is nonmeasurable with respect to a fixed ideal $\bbi$ with Borel base of a fixed uncountable Polish space. Our result applies to the classical ideal of null subsets of the real line and to the ideal of first category subsets of the real line.

arXiv comment8 pages, accepted to Math. Log. Quart