Duality of Measure and Category in Infinite-dimensional Separable Hilbert Space
نویسنده
چکیده
As usual, we equip an infinite-dimensional separable Hilbert space 2 by such nonzero σ -finite Borel measures which are invariant with respect to everywhere dense vector subspaces and study duality between such measures and Baire category. Section 1 contains constructions of nontrivialσ -finite Borel measures, which are defined in the infinite-dimensional separable Hilbert space 2 and are invariant with respect to some everywhere dense vector subspaces. The duality between invariant Borel measures and Baire category in the classical Hilbert space 2 is studied in Section 2. An idea applied in the process of proving of the main assertions allows us to obtain more general results for sufficiently large class of infinite-dimensional topological vector spaces.
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