On quasi-invariant measures in topological vector spaces | Zendy

H. Hogbe Nlend | Zendy

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On quasi-invariant measures in topological vector spaces

Author(s) -

H. Hogbe Nlend

Publication year - 1997

Publication title -

bulletin of the belgian mathematical society - simon stevin

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.36

H-Index - 31

eISSN - 2034-1970

pISSN - 1370-1444

DOI - 10.36045/bbms/1105737764

Subject(s) - mathematics , invariant (physics) , pure mathematics , topological tensor product , locally convex topological vector space , hilbert space , banach space , measure (data warehouse) , vector space , interpolation space , fréchet space , topological vector space , mathematical analysis , topology (electrical circuits) , topological space , functional analysis , combinatorics , computer science , mathematical physics , biochemistry , chemistry , database , gene

We give a complete solution of the fundamental problem of existence of quasi-invariant measures in innite dimensional vector spaces considered and partially solved by I.M. Gelfand in 1967 [4]. Our general result shows particularly that in all innite dimensional usual vector spaces, in particular,in all Fr echet, Banach or Hilbert spaces and in all spaces of distributions, the only quasi-invariant measure is null measure.

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