Complete nonmeasurability in regular families

• Autores: Robert Ralowski
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 34, Nº 3, 2008, págs. 773-780
• Idioma: inglés
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• Resumen

  • We show that for a sigma-ideal I with a Borel base of subsets of an uncountable Polish space, if A is (in several senses) a "regular" family of subsets from I then there is a subfamily of A whose union is completely nonmeasurable i.e. its intersection with every Borel set not in I does not belong to the smallest sigma-algebra containing all Borel sets and I. Our results generalize results obtained by Brzuchowski, Cichon, Grzegorek, Ryll-Nardzewski and the authors of this paper.