Advertisement

On Prohorov’s Criterion for Projective Limits

  • Erik G. F. Thomas
Part of the Operator Theory: Advances and Applications book series (OT, volume 168)

Abstract

We propose a modification of Prohorov’s theorem on projective limits of Radon measures which can be directly applied to the construction of Wiener measure on the space of continuous functions, and we give such a construction.

Keywords

Compact Subset Radon Measure Projective Limit Compatible System Wiener Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    N. Bourbaki, Intégration, Ch. IX, Hermann, Paris, 1969.Google Scholar
  2. [2]
    N. Bourbaki, Topologie Générale, Troisième Edition, Ch. 1, Hermann, Paris, 1961.Google Scholar
  3. [3]
    E. Nelson, Feynman integral and the Schrödinger equation, J. Math. Phys. 5, 332–343, 1964.zbMATHCrossRefGoogle Scholar
  4. [4]
    E. Nelson, Regular probability measures on functions space, Annals of Math., 69, 1959, pp. 630–643.zbMATHCrossRefGoogle Scholar
  5. [5]
    Ju.V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Theory. Prob. Appl., t. I (1956), pp. 156–214.Google Scholar
  6. [6]
    L. Schwartz, Radon Measures on Arbitrary Topological Spaces, and cylindrical measures, Oxford Univ. Press 1973.Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Erik G. F. Thomas
    • 1
  1. 1.Department of MathematicsUniversity of GroningenGroningenThe Netherlands

Personalised recommendations