Pacific Journal of Mathematics

Scale-invariant measurability in abstract Wiener spaces.

Dong Myung Chung

Article information

Pacific J. Math., Volume 130, Number 1 (1987), 27-40.

First available in Project Euclid: 8 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11]
Secondary: 46G12: Measures and integration on abstract linear spaces [See also 28C20, 46T12] 60B11: Probability theory on linear topological spaces [See also 28C20] 60F17: Functional limit theorems; invariance principles


Chung, Dong Myung. Scale-invariant measurability in abstract Wiener spaces. Pacific J. Math. 130 (1987), no. 1, 27--40.

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  • [1] R.H.Cameron, The translationpathology of Wiener space, Duke Math. J.,21(1954), 623-628.
  • [2] R. H.Cameron and W. T.Martin, The behavior of measure andmeasurability under change of scale in Wiener space, Bull. Amer. Math. Soc, 53(1947), 130-137.
  • [3] K. S. Chang, Scale-invariant measurability infunction space, Thesis, University of Nebraska, Lincoln, Neb., 1979.
  • [4] D. L.Cohn, Measure Theory, Birkhauser, Boston, 1980.
  • [5] P.Halmos, Measure Theory, Van Nostrand,New York, 1950.
  • [6] G. W. Johnson andD. L. Skoug, Scale-invariant measurability in Wiener space, Pacific J. Math, 83(1979), 157-176.
  • [7] G. Kallianpur and C. Bromley, Generalized Feynman Integrals Using Analytic Continuation in Several Complex Variables, Stochastic Analysis, M. Pinsky, ed, Marcel-Dekker, 1984.
  • [8] H. H. Kuo, Gaussian Measures in Banach Spaces, Lecture Notes in Mathematics, No. 463, Springer, Berlin, 1975.
  • [9] J. Kuelbs, Abstract Wiener spaces and applications to analysis, Pacific J. Math., 31 (1969), 433-450.
  • [10] D. L. Skoug, Converses to measurability theorems for Yeh-Wiener space, Proc. Amer. Math. Soc, 57 (1976), 304-310.
  • [11] D. L. Skoug, The change of scale and translation pathology in Yeh-Wiener space, Riv. Math. Univ. Parma, 3 (1977), 79-87.
  • [12] J. Yeh, Stochastic Processes and the Wiener Integral, Marcel Dekker, New York, 1973.
  • [13] J. Yeh, Wiener measure in a space of functions of two variables, Trans. Amer. Math. Soc, 95 (1960), 433-450.