Surface Measures and Tightness of ( r, p)-Capacities on Poisson Space

We prove tightness of ( r, p)-Sobolev capacities on configuration spaces equipped with Poisson measure. By using this result we construct surface measures on configuration spaces in the spirit of the Malliavin calculus. A related Gauss–Ostrogradskii formula is obtained.

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Bibliographic Details
Published in:Journal of functional analysis 2002-12, Vol.196 (1), p.61-86
Main Authors: Bogachev, V.I., Pugachev, O.V., Röckner, M.
Format: Article
Language:English
Subjects:
capacity
configuration space
Gauss–Ostrogradskii formula
Sobolev classes
surface measure
tightness
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Description
Summary:We prove tightness of ( r, p)-Sobolev capacities on configuration spaces equipped with Poisson measure. By using this result we construct surface measures on configuration spaces in the spirit of the Malliavin calculus. A related Gauss–Ostrogradskii formula is obtained.
ISSN:0022-1236
1096-0783
DOI:10.1006/jfan.2002.3962