Geodesic
Spaces of quasi-invariance of product measures
Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 2, pp. 79-81

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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 $1\le q 2$.
Keywords: space of quasi-invariance, space of equivalent shifts, Shepp's theorem, product measure. 
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     author = {L. M. Arutyunyan and E. D. Kosov},
     title = {Spaces of quasi-invariance of product measures},
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L. M. Arutyunyan; E. D. Kosov. Spaces of quasi-invariance of product measures. Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 2, pp. 79-81. http://geodesic.mathdoc.fr/item/FAA_2015_49_2_a7/