×

zbMATH — the first resource for mathematics

Non-Borel measures on non-separable metric spaces. (English) Zbl 0755.28002
Aspects of the theory of non-Borel measures on non-separable metric spaces due to R. M. Dudley and D. Polard are investigated by means of the theory of finitely additive set functions according to A. D. Alexandroff.

MSC:
28A10 Real- or complex-valued set functions
28A33 Spaces of measures, convergence of measures
60B05 Probability measures on topological spaces
PDF BibTeX XML Cite
Full Text: EuDML
References:
[1] ALEXANDROFF A. D.: Additive set functions in abstract spaces. Mat. Sb. 8, 1940, 307-348; 9, 1941, 563-628; 13, 1943, 169-238. · Zbl 0023.39701
[2] BOURBAKI N.: Éléments de mathématiques. Livre VI, Intégration, Hermann, Paris 1959-1969. · Zbl 0102.25503
[3] LE-CAM L.: Convergence in distribution of stochastic processes. Univ. California Publ. Statist. 2, no. 11, 1957, 207-236. · Zbl 0077.12301
[4] DUDLEY R. M.: Weak convergence of probabilities on nonseparable metric spaces and empirical measures on Euclidean spaces. Illinois J. Math. vol 10, 1966, 109-126. · Zbl 0178.52502
[5] DUDLEY R. M.: Measures on non-separable metric spaces. Illinois J. Math. vol 11, 1967, 449-453. · Zbl 0152.24501
[6] ENGELKING R.: General Topology. PWN, Warszawa 1977. · Zbl 0373.54002
[7] FREMLIN D. H., GARLING G. J. H., HAYDON R. G.: Bounded measures on topological spaces. Proc. London Math. Soc. 3, no. 25, 1972, 115-136. · Zbl 0236.46025
[8] HALMOS P. R.: Measure Theory. D. Van Nostrand, New York 1950. · Zbl 0040.16802
[9] KELLEY J. L.: General Topology. D. Van Nostrand, New York 1955. · Zbl 0066.16604
[10] PACHL J. K.: Measures as functionals on uniformly continuous functions. Pacific. J. Math. 82, no. 2, 1979, 515-521. · Zbl 0419.28006
[11] POLLARD D.: Weak convergence on non-separable metric spaces. J. Austral. Math. Soc. 28, 1979, 197-204. · Zbl 0423.60005
[12] POLLARD D., TOPSØE F.: A unified approach to the Riesz type representation theorems. Studia Math. 54, 1975, 173-190. · Zbl 0321.28006
[13] TOPSØE F.: Topology and Measure. Springer, Berlin 1970. · Zbl 0197.33301
[14] TOPSØE F.: Compactness in spaces of measures. Studia Math. 36, 1970, 195-212. · Zbl 0201.06202
[15] TOPSØE F.: Further results on integral representations. Studia Math. 55, 1976, 239-245. · Zbl 0336.28002
[16] VARADARJAN V. S.: Measures on topological spaces. Mat. Sb. 55, 1961, 35-100.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.