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Potential Analysis

, Volume 44, Issue 4, pp 767–792 | Cite as

Surface Measures Generated by Differentiable Measures

  • Vladimir I. BogachevEmail author
  • Ilya I. Malofeev
Article

Abstract

We study surface measures on level sets of functions on general probability spaces with measures differentiable along vector fields and suggest a new simple construction. Our construction applies also to level sets of mappings with values in finite-dimensional spaces. The standard surface measures arising for Gaussian measures in the Malliavin calculus can be obtained in this way. A positive answer is given to a question raised by M. Röckner concerning continuity of surface measures with respect to a parameter.

Keywords

Malliavin calculus Surface measure Differential measure Gaussian measure 

Mathematics Subject Classification (2010)

28C20 46G12 60H07 60B11 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsMoscowRussia
  2. 2.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia

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