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Dirichlet spaces on H-convex sets in Wiener space
We consider the -Sobolev space on subsets in an
abstract Wiener space, which is regarded as a canonical Dirichlet space on .
We prove that has smooth cylindrical functions as a dense subset
if is -convex and -open. For the proof, the relations between
-notions and quasi-notions are also studied.Comment: 18 pages, 1 figure. Erratum has been added, which was accepted for
publication in Bull. Sci. Mat
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