# Convergence of compound probability measures on topological spaces

Colloquium Mathematicae (1994)

- Volume: 67, Issue: 2, page 161-176
- ISSN: 0010-1354

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topKawabe, Jun. "Convergence of compound probability measures on topological spaces." Colloquium Mathematicae 67.2 (1994): 161-176. <http://eudml.org/doc/210269>.

@article{Kawabe1994,

author = {Kawabe, Jun},

journal = {Colloquium Mathematicae},

keywords = {Gaussian transition probabilities; continuous transition probabilities; compound probability measures; equicontinuity; weak convergence; information theory; convolution measures; Prokhorov's compactness criterion for probability measures; uniform tightness of compound probability measures},

language = {eng},

number = {2},

pages = {161-176},

title = {Convergence of compound probability measures on topological spaces},

url = {http://eudml.org/doc/210269},

volume = {67},

year = {1994},

}

TY - JOUR

AU - Kawabe, Jun

TI - Convergence of compound probability measures on topological spaces

JO - Colloquium Mathematicae

PY - 1994

VL - 67

IS - 2

SP - 161

EP - 176

LA - eng

KW - Gaussian transition probabilities; continuous transition probabilities; compound probability measures; equicontinuity; weak convergence; information theory; convolution measures; Prokhorov's compactness criterion for probability measures; uniform tightness of compound probability measures

UR - http://eudml.org/doc/210269

ER -

## References

top- [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. Zbl0538.60006
- [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. Zbl0247.43005
- [4] X. Fernique, Processus linéaires, processus généralisés, Ann. Inst. Fourier (Grenoble) 17 (1) (1967), 1-92. Zbl0167.16702
- [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. Zbl0137.11301
- [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. Zbl0298.28001
- [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. Zbl0255.47012
- [12] N. N. Vakhania, V. I. Tarieladze and S. A. Chobanyan, Probability Distributions on Banach Spaces, D. Reidel, 1987.

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