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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
Mathematics

Abstract

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.

Keywords

Hilbert Space DOKLADY Mathematic Gaussian Measure Canonical Embedding Infinite Dimensional Space 
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.

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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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