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Spaces of quasi-invariance of product measures. (English. Russian original) Zbl 1342.46041

Funct. Anal. Appl. 49, No. 2, 142-144 (2015); translation from Funkts. Anal. Prilozh. 49, No. 2, 79-81 (2015).
Summary: Classical results of Shepp and Feldman give a criterion for a product measure which is a countable power of a measure on \(\mathbb{R}\) with positive density to be equivalent to its shift by any vector in \(\ell^2\). In this work, a similar problem is studied for shifts of a measure by vectors in \(\ell^q\) for \(1 \leqslant q < 2\).

MSC:

46G12 Measures and integration on abstract linear spaces
28A35 Measures and integrals in product spaces
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References:

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[2] Feldman, J., No article title, Trans. Amer. Soc., 99, 342-349 (1961) · Zbl 0111.32305
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