Two results for monocompact measures (Q1313562)

The author proves that a finite measure defined on an \(\omega_ 1\)- generated \(\sigma\)-algebra of sets is monocompact if and only if it is compact [this gives a partial answer to a question of \textit{F. Topsøe} posed in Colloq. Math. 42, 377-385 (1979; Zbl 0448.28001), whether monocompact measures are compact]. As a consequence, the author gets the result that an example constructed by the reviewer in Lect. Notes Math. 541, 31-42 (1976; Zbl 0341.28003) of a perfect but non-compact measure is in fact an example of a perfect and not monocompact measure (this answers another question of Topsøe [also \textit{D. Ramachandran}, ``Perfect measures. II'' (1979; Zbl 0523.60006)], whether the notions of perfectness and monocompactness are equivalent). That monocompactness implies perfectness was proved earlier by Pachl (\textit{F. Topsøe}, ibid.).