All Meager Filters may be Null
Tomek Bartoszyński, Martin Goldstern, Haim I. Judah, Saharon Shelah · Proceedings of the American Mathematical Society · 1993
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.