Vol. 96, No. 2, 1981

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Some topological properties of spaces of measures

Georgios Koumoullis

Vol. 96 (1981), No. 2, 419–433

Let X be a completely regular space and Mτ(X), Mt(X) and Mc(X) the spaces of the τ-additive measures, tight measures and measures with compact support on X, endowed with the weak topology. The aim of this paper is to study topological properties that devolve from X to Mτ(X), Mt(X) and Mc(X) or their positive cones Mτ+(X), Mt+(X) and Mc+(X). It is proved that if X is paracompact (resp. Lindelöf) and Cech complete, then Mτ+(X) and Mt+(X) have the same properties, but Mc+(X) does not (unless X is compact). If X is realcompact then Mc(X) has the same property, but Mτ(X) and Mt(X) need not. However, if X is realcompact paracompact, then Mτ(X) is realcompact.

Mathematical Subject Classification 2000
Primary: 46E27
Secondary: 28A33, 54D99
Received: 20 June 1980
Published: 1 October 1981
Georgios Koumoullis