This article is cited in 5 papers

Short Communications

Capacities and Surface Measures in Locally Convex Spaces

O. V. Pugachev

N. E. Bauman Moscow State Technical University

Abstract: We prove tightness of capacities generated by Sobolev classes of any order in a wide class of locally convex spaces. These capacities are applied in constructing surface measures on level sets of Sobolev and local Sobolev functions.

Keywords: differentiable measure, Sobolev classes in locally convex spaces, tightness of capacity, surface measure, Gauss–Ostrogradskii formula, local Sobolev functions.

Received: 13.06.2007

DOI: 10.4213/tvp2493

 English version: Theory of Probability and its Applications, 2009, 53:1, 179–190

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