Generalizations of Gross' and Minlos' theorems

  • Jia An Yan
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1372)


The purpose of this note is to give simple proofs, with some extensions, of the well known theorems of Gross, Dudley-Feldman-LeCam and Minlos, and also of the general version of Gross' theorem given by Lindstrøm.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Badrikian A., Séminaire sur les Fonctions Aléatoires Linéaires et les Mesures Cylindriques, Lect. Notes in M. 139, Springer 1970.Google Scholar
  2. [2]
    Dudley R.M., Feldman J., LeCam L., On semi-norms and probabilities, and abstract Wiener spaces, Ann. M. 93, 1971, p. 390–408.MathSciNetCrossRefGoogle Scholar
  3. [3]
    Gross L., Abstract Wiener Spaces, Proc. 5-th Berkeley Symp. Math. Stat. and Prob. 2, 1965, p. 31–42.Google Scholar
  4. [4]
    Hida T., Brownian Motion, Springer 1980.Google Scholar
  5. [5]
    Kallianpur G., Abstract Wiener processes and their reproducing kernel Hilbert spaces. ZW 17, 1971, p. 113–123.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Kuo H.H., Gaussian Measures on Banach Spaces, Lect. Notes in M. 463, Springer 1975.Google Scholar
  7. [7]
    Lindström T.L., A Loeb-measure approach to theorems by Prokhorov, Sazonov and Gross. Trans. Amer. Math. Soc. 269, 1982, p. 521–534.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Vakhania N.N., Tarieladge V.I., Chobanyan S.A., Probability Distributions on Banach Spaces, Reidel Publ. Co, Dordrecht 1987.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Jia An Yan
    • 1
  1. 1.Institute of Applied MathematicsAcademia SinicaBeijing

Personalised recommendations