Descriptive properties of spaces of measures

• Autorzy: Holicky P. , Kalenda O.
• Języki publikacji: EN

Abstrakty

EN

The spaces of Borel probabilities on a topological space X inherit a number of topological properties of X. We show in particular that the space of tight probabilities on a Cech-analytic space is Cech-analytic. Analogical results are shown for several other classes of generalized analytic and complete topological spaces.

Słowa kluczowe

EN

analytic space; Borel measure; complete space; sigma-scattered network; Σ-scattered network; weak topology

PL

przestrzeń analityczna; topologia

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1999
• Tom: Vol. 47, no 1
• Strony: 37--51
• Opis fizyczny: Bibliogr. 13 poz.,

Twórcy

autor

Holicky P.

• Department of Mathematical Analysis, Charles University, Sokolovska 83, 186 75, Prague 8, Czech Republic

autor

Kalenda O.

• Department of Mathematical Analysis, Charles University, Sokolovska 83, 186 75, Prague 8, Czech Republic

Bibliografia

• [1] L. Schwartz, Radom Measures, Oxford University Press, London 1973.
• [2] F. Topseøe, Topology and Measure, Lect. Notes Math., 133, Springer-Verlag
• [3] C. A. Rogers, Hausdorff Measures, Cambridge University Press 1970.
• [4] A. S. Kechris, Classical Descriptive Set Theory, Springer-Verlag 1995.
• [5] R. W. Hansell, Descriptive sets and the topology of non-separable Banach, spaces, preprint 1989.
• [6] P. Holický, Luzin theorems for scattered-K-analytic spaces and Borel measures on them, Atti Sem. Mat. Fis. Univ. Modena, 44 (1996) 395-413.
• [7] C. Koumoullis, A generalization of functions of the first class, Topology and its Applications, 50 (1993) 217-239.
• [8] R. J. Gardner, W. F. Pfeffer, Borel measures, in: Handbook of set-theoretic topology, eds: K. Kunen, J. E. Vaughan, North-Holand (1984) 961-1043.
• [9] V. S. Varadarajan, Measures on topological spaces (in Russian), Mat. Sb. (N.S.) 55 (1961) 35-100.
• [10] R. W. Hansell, Descriptive topology, in: Recent progress in general topology, eds: M. Hušek, J. van Mill, North-Holland (1992) 275-315.
• [11] P. P. Holický, Cech-analytic and almost-K-descriptive spaces, Czech. Math. J., 43 (1993). 451-466.
• [12] P. Holický , Generalized analytic spaces and fraymentability, to be published.
• [13] Z. Frolík, A survey of separable descriptive theory of sets and spaces, Czechoslovak Math. J., 20 (1970) 406-467.