On spaces of σ-additive probability measures

The functor Pσ of σ-additive probability measures on the category of Tychonoff spaces is investigated. It is shown that the space Pσ(X) is Hewitt complete for every Tychonoff space X; and Pσ(X) is an AE-space of weight ⩽ω1 iff Pσ(X) is an AE(0)-space of weight ⩽ω1 iff the Hewitt completion of X is an AE(0)-space of weight ⩽ω1. It is shown that for every separable metrizable absolute Borel space X the space Pσ(Xω1) is homeomorphic to Pσ(X)ω1. In particular, Pσ(Rω1) is homeomorphic to Rω1. We find conditions on a Tychonoff (uniform) space X under which Pσ(X) is a Hewitt completion (respectively is naturally homeomorphic to the completion) of the (uniform) spaces PR(X) and Pτ(X) of Radon and τ-additive probability measures on X.