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[en] We prove that the functors PR and Pτ of Radon and τ-additive probability measures, respectively, preserve neither the real-completeness nor the Dieudonne completeness of Tychonoff spaces. We suggest conditions under which Martin's axiom implies that Pτ preserves real-complete spaces, absolute extensors, and Tychonoff bundles. These last results cannot be obtained without additional set-theoretic assumptions
Journal
Izvestiya. Mathematics; ISSN 1064-5632; 
; v. 63(4); p. 827-843
; v. 63(4); p. 827-843