Convergence of compound probability measures on topological spaces

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

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

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.
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.
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.
X. Fernique, Processus linéaires, processus généralisés, Ann. Inst. Fourier (Grenoble) 17 (1) (1967), 1-92.
P. R. Halmos, Measure Theory, Van Nostrand, Princeton, 1950.
J. L. Kelley, General Topology, Van Nostrand, New York, 1955.
J. Neveu, Mathematical Foundations of the Calculus of Probability, Holden-Day, San Francisco, 1965.
Yu. V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Theory Probab. Appl. 1 (1956), 157-214.
L. Schwartz, Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures, Oxford University Press, 1973.
F. Topsοe, Topology and Measure, Lecture Notes in Math. 133, Springer, Berlin, 1970.
H. Umegaki, Representations and extremal properties of averaging operators and their applications to information channels, J. Math. Anal. Appl. 25 (1969), 41-73.
N. N. Vakhania, V. I. Tarieladze and S. A. Chobanyan, Probability Distributions on Banach Spaces, D. Reidel, 1987.