We show that it is consistent with ZFC that all filters which have the Baire property are Lebesgue measurable. We also show that the existence of a Sierpinski set implies that there exists a nonmeasurable filter which has the Baire property. The goal of this paper is to show yet another example of nonduality between measure and category. Suppose that F is a nonprincipal filter on ω. Identify F ...

We study Baire category for downward-closed subsets of 2ω , showing that it behaves better in this context than for general subsets of 2ω . We show that, in the downward-closed context, the ideal of meager sets is prime and b-complete, while the complementary filter is g-complete. We also discuss other cardinal characteristics of this ideal and this filter, and we show that analogous results fo...

The Kestelman-Borwein-Ditor Theorem asserts that a non-negligible subset of R which is Baire (= has the property, BP) or measurable shift-compact: it contains some subsequence any null sequence to within translation by an element set. Here effective proofs are recognized yield (i) analogous category and Haar-measure metrizable generalizations for groups locally compact respectively, (ii) permit...

The purpose of this chapter is to discuss various results concerning the relationship between measure and category. We are mostly interested in set-theoretic properties of these ideals, particularly, their cardinal characteristics. This is a very large area, and it was necessary to make some choices. We decided to present several new results and new approaches to old problems. In most cases we ...