Convergence of compound probability measures on topological spaces

Jun Kawabe

Colloquium Mathematicae (1994)

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

How to cite

top

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

top
  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. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.