On the measurability problem for category bases (Q1189077)

The concept of category bases unifies properties of Lebesgue measure and Baire category. However, if we consider larger measure spaces, not all of them can be represented in the frame of this concept. In the paper the author shows (under the assumption that there are no measurable cardinals) that in the class of all complete measure spaces with the \(ccc\) subset property exactly the \(ccc\) decomposable ones can be represented by some category base. A second characterization for \textit{finite} subset property spaces is also given.