Category measures on Baire spaces
A category measure in a topological space is a finite, countably additive measure m defined on the class of sets having the Baire property and such that \(m(E)=0\) if and only if E is of first category. In this article, the author proves a necessary and sufficient condition for a Baire space to admit a category measure. In the last section of the article, the author cites several classes of topological spaces which admit category masures, but all of them appear to be trivial examples. The space given in Example 1.1 turns out to be the topological sum of finitely many indiscrete spaces, while the spaces mentioned in Examples 3.2 and 3.3 and in Propositions 3.1, 3.2 and 3.3 are finite discrete spaces. The latter follows easily from the fact every first countable extremally disconnected Hausdorff space is discrete. (see e.g. \textit{Albert Wilansky}, Topology for analysis (1970; Zbl 0229.54001, Theorem 14.1.5).
scientific article; zbMATH DE number 4194682