Remarks on nonmeasurable unions of big point families

Details Remarks on nonmeasurable unions of big point families Remarks on nonmeasurable unions of big point families

2010-01-04

arxiv.org/abs/1001.0549v1

Mathematial Logic Quarterly, vol 55, nr 6 (2009) pp. 659-665

Mathematics

General Topology

8 pages, accepted to Math. Log. Quart

Scientific paper

10.1002/malq.200810014

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.

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