Convergence of compound probability measures on topological spaces

• Autorzy: Jun Kawabe
• Języki publikacji: EN

Słowa kluczowe

EN

Gaussian transition probabilities; continuous transition probabilities; compound probability measures; equicontinuity

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1994
• Tom: 67
• Numer: 2
• Strony: 161-176

Daty

wydano

1994

otrzymano

1993-05-24

Twórcy

autor

Jun Kawabe

• Department of Mathematics, Faculty of Engineering, Shinshu University, Wakasato, Nagano 380, Japan

Bibliografia

• [1] S. Chevet, Compacité dans l'espace des probabilités de Radon gaussiennes sur un Banach, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), 275-278.
• [2] I. Csiszár, Some problems concerning measures on topological spaces and convolutions of measures on topological groups, in: Les Probabilités sur les Structures Algébriques, Clermont-Ferrand, Colloq. Internat. CNRS, Paris, 1969, 75-96.
• [3] I. Csiszár, On the weak* continuity of convolution in a convolution algebra over an arbitrary topological group, Studia Sci. Math. Hungar. 6 (1971), 27-40.
• [4] X. Fernique, Processus linéaires, processus généralisés, Ann. Inst. Fourier (Grenoble) 17 (1) (1967), 1-92.
• [5] P. R. Halmos, Measure Theory, Van Nostrand, Princeton, 1950.
• [6] J. L. Kelley, General Topology, Van Nostrand, New York, 1955.
• [7] J. Neveu, Mathematical Foundations of the Calculus of Probability, Holden-Day, San Francisco, 1965.
• [8] Yu. V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Theory Probab. Appl. 1 (1956), 157-214.
• [9] L. Schwartz, Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures, Oxford University Press, 1973.
• [10] F. Topsοe, Topology and Measure, Lecture Notes in Math. 133, Springer, Berlin, 1970.
• [11] H. Umegaki, Representations and extremal properties of averaging operators and their applications to information channels, J. Math. Anal. Appl. 25 (1969), 41-73.
• [12] N. N. Vakhania, V. I. Tarieladze and S. A. Chobanyan, Probability Distributions on Banach Spaces, D. Reidel, 1987.