Resumen de Complete nonmeasurability in regular families

Robert Ralowski

• 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.