Convergence of compound probability measures on topological spaces

Jun Kawabe

Colloquium Mathematicae (1994)

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

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Kawabe, 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

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  1. [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. [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. [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. [4] X. Fernique, Processus linéaires, processus généralisés, Ann. Inst. Fourier (Grenoble) 17 (1) (1967), 1-92. Zbl0167.16702
  5. [5] P. R. Halmos, Measure Theory, Van Nostrand, Princeton, 1950. 
  6. [6] J. L. Kelley, General Topology, Van Nostrand, New York, 1955. 
  7. [7] J. Neveu, Mathematical Foundations of the Calculus of Probability, Holden-Day, San Francisco, 1965. Zbl0137.11301
  8. [8] Yu. V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Theory Probab. Appl. 1 (1956), 157-214. 
  9. [9] L. Schwartz, Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures, Oxford University Press, 1973. Zbl0298.28001
  10. [10] F. Topsοe, Topology and Measure, Lecture Notes in Math. 133, Springer, Berlin, 1970. 
  11. [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. [12] N. N. Vakhania, V. I. Tarieladze and S. A. Chobanyan, Probability Distributions on Banach Spaces, D. Reidel, 1987. 

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