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On Partial Integration in Infinite‐Dimensional Space and Applications to Dirichlet Forms
Author(s) -
Albeverio Sergio,
Kusuoka Shigeo,
Röckner Michael
Publication year - 1990
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-42.1.122
Subject(s) - mathematics , dirichlet distribution , regular polygon , probability measure , pure mathematics , space (punctuation) , measure (data warehouse) , invariant (physics) , locally convex topological vector space , characterization (materials science) , convex set , mathematical analysis , topological space , convex optimization , computer science , geometry , physics , boundary value problem , database , optics , mathematical physics , operating system
Let E be a locally convex (Souslinean) topological vector space and μ an arbitrary (not necessarily quasi‐invariant) probability measure on E . We prove a characterization of the set of all k ∈ E ∖{0} for which a partial integration formula holds for the corresponding derivative δ/δ k . As a consequence we improve a recent result by two of the authors on the maximality problem for classical Dirichlet forms.