On an invariant Borel measure in Hilbert space

• Autorzy: Pantsulaia G.
• Języki publikacji: EN

Abstrakty

EN

An example of a nonzero [sigma]-finite Borel measure [my] with everywhere dense linear manifold I[my] of admissible (in the sense of invariance) translation vectors is constructed in the Hilbert space l[2] such that [my] and any shift [my]^[alpha] of [my] by a vector [alpha] is an element of l[2] \ I[my] are neither equivalent nor orthogonal. This extends a result established in [7].

Słowa kluczowe

EN

admissible translation; Gaussian measure; quasi-invariance; invariance

PL

translacja dopuszczalna; miara Gaussa; quasi-niezmienniczość; niezmienniczość

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 1
• Strony: 47--51
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Pantsulaia G.

Bibliografia

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• [3] -, -, Transformations of Wiener integrals under a general class of linear transformations, Trans. Amer. Math. Soc. 58 (1945), 184-219.
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• [9] P. R. Halmos, Measure Theory, Van Nostrand, New York, 1950.
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