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.
