Doklady Mathematics

, Volume 92, Issue 3, pp 743–746 | Cite as

Invariant and quasi-invariant measures on infinite-dimensional spaces

  • V. V. Kozlov
  • O. G. Smolyanov


Extensions of locally convex topological spaces are considered such that finite cylindrical measures which are not countably additive on their initial domains turn out to be countably additive on the extensions. Extensions of certain transformations of the initial spaces with respect to which the initial measures are invariant or quasi-invariant to the extensions of these spaces are described. Similar questions are considered for differentiable measures. The constructions may find applications in statistical mechanics and quantum field theory.


Hilbert Space DOKLADY Mathematic Gaussian Measure Canonical Embedding Infinite Dimensional Space 
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  1. 1.
    V. V. Kozlov, Russ. Math. Surv., 63 (4), 691–726 (2008).zbMATHCrossRefGoogle Scholar
  2. 2.
    O. G. Smolyanov and S. V. Fomin, Russ. Math. Surv. 31 (4), 1–53 (1976).zbMATHCrossRefGoogle Scholar
  3. 3.
    O. G. Smolyanov and E. T. Shavgulidze, Continual Integrals, 2nd ed. (URRS, Moscow, 2015) [in Russian].Google Scholar
  4. 4.
    V. I. Bogachev and O. G. Smolyanov, Russ. Math. Surv. 45 (3), 1–104 (1990).zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    V. I. Bogachev, Differentiable Measures and the Malliavin Calculus (Am. Math. Soc., Providence, R.I., 2010).zbMATHCrossRefGoogle Scholar
  6. 6.
    O. G. Smolyanov, Dokl. Akad. Nauk SSSR 170 (3), 526–529 (1966).MathSciNetGoogle Scholar
  7. 7.
    J. Kupsch and O. G. Smolyanov, Math. Notes 68 (3), 409–414 (2000).zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    N. Dunford and J. Schwartz, Linear Operators, Vol. 1: General Theory (Interscience, New York, 1958).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Steklov Institute of MathematicsRussian Academy of SciencesMoscowRussia
  2. 2.Mechanics and Mathematics FacultyMoscow State UniversityMoscowRussia

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