Geodesic
Topological completeness of spaces of measures
Izvestiya. Mathematics , Tome 63 (1999) no. 4, pp. 827-843

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We prove that the functors $P_R$ and $P_\tau$ of Radon and $\tau$-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 $P_\tau$ preserves real-complete spaces, absolute extensors, and Tychonoff bundles. These last results cannot be obtained without additional set-theoretic assumptions. 
@article{IM2_1999_63_4_a8,
     author = {V. V. Fedorchuk},
     title = {Topological completeness of spaces of measures},
     journal = {Izvestiya. Mathematics },
     pages = {827--843},
     publisher = {mathdoc},
     volume = {63},
     number = {4},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1999_63_4_a8/}
}
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V. V. Fedorchuk. Topological completeness of spaces of measures. Izvestiya. Mathematics , Tome 63 (1999) no. 4, pp. 827-843. http://geodesic.mathdoc.fr/item/IM2_1999_63_4_a8/