Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-06-09T00:47:52.723Z Has data issue: false hasContentIssue false
  • English
  • Français

Topological Properties of Limits of Inverse Systems Of Measures

Published online by Cambridge University Press:  20 November 2018

Donald J. Mallory
Donald J. Mallory*
Affiliation:
Simon Fraser University, Burnaby, British Columbia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It has been shown (Mallory and Sion [6]) that the problem of finding "limit" measures for inverse systems of measure spaces (Xi, μi)i∊I can be successfully attacked by establishing the existence of a “limit” measure on the product space , then considering the restriction to the inverse limit set .

In this paper we use a similar point of view to establish conditions under which a system of Radón measures has a “limit” measure which is also Radón.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 6 , December 1974 , pp. 1455 - 1465
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Bourbaki, N., Intégration, Livre VI, Ch. IX (Hermann, Paris, 1969).Google Scholar
2. Choksi, J. R., Inverse limits of measure spaces, Proc. London Math. Soc. 8 (1958), 321–342.Google Scholar
3. Jirina, M., Conditional probabilities on strictly separable σ-algebra, (Russian) Czechoslovak Math. J. 4 (1954), 372–80.Google Scholar
4. Kisyński, J., On the generation of tight measures, Studia Math. 30 (1968), 141–151.Google Scholar
5. Mallory, D. J., Limits of inverse systems of measures, Ph.D. thesis, University of British Columbia, 1968.Google Scholar
6. Mallory, D. J. and M. Sion, Limits of inverse systems of measures, Ann. Inst. Fourier (Grenoble) 21 (1971), 25–57.Google Scholar
7. Metivier, M., Limites projectives de mesures, martingales applications, Ann. di Mathematica 63 (1963), 225–352.Google Scholar
8. Prokhorov, Yu. V., Convergence of random processes and limit theorems of probability theory (in Russian), Teor. Verojatnos. i Primenen. 1, (1956), 177-237. English translation: Theor. Probability Appl. 1, (1956), 157–214.Google Scholar
9. Scheffer, C. L., Projective limits of directed projective systems of probability spaces, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 13 (1969), 60–80.Google Scholar
10. Sion, M., Lecture notes on measure theory, Biennial Seminar of the Canadian Mathematical Congress, 1965.Google Scholar
11. Sion, M., Introduction to the methods of real analysis (Holt, Rinehart and Winston, New York, 1968).Google Scholar