Abstract
AbstractAssume that there is no quasi‐measurable cardinal not greater than 2ω . We show that for a c. c. c. σ ‐ideal 𝕀 with a Borel base of subsets of an uncountable Polish space, if 𝒜 is a point‐finite family of subsets from 𝕀, then there is a subfamily of 𝒜 whose union is completely nonmeasurable, i.e. its intersection with every non‐small Borel set does not belong to the σ ‐field generated by Borel sets and the ideal 𝕀. This result is a generalization of the Four Poles Theorem (see [1]) and a result from [3]. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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