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 Mat. Sb. (N.S.), 1985, Volume 127(169), Number 3(7), Pages 336–351 (Mi msb2000)

Some results on differentiable measures

V. I. Bogachev

Abstract: Connections are described between various differentiability properties of measures on locally convex spaces. In particular, it is proved that every analytic measure is quasi-invariant, and every quasi-invariant measure is absolutely continuous with respect to some analytic measure. It is proved that for stable measures continuity in some direction implies infinite differentiability, and even analyticity in this direction when $\alpha\geqslant1$. A solution is presented for a problem posed by Aronszajn (RZh.Mat., 1977, 5B557).
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Sbornik, 1986, 55:2, 335–349

Bibliographic databases:

UDC: 517.98
MSC: Primary 28A15, 28C15, 46G12; Secondary 28C20, 46A05, 46G10, 60B11, 60E07

Citation: V. I. Bogachev, “Some results on differentiable measures”, Mat. Sb. (N.S.), 127(169):3(7) (1985), 336–351; Math. USSR-Sb., 55:2 (1986), 335–349

Citation in format AMSBIB
\Bibitem{Bog85} \by V.~I.~Bogachev \paper Some results on differentiable measures \jour Mat. Sb. (N.S.) \yr 1985 \vol 127(169) \issue 3(7) \pages 336--351 \mathnet{http://mi.mathnet.ru/msb2000} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=798381} \zmath{https://zbmath.org/?q=an:0597.46043} \transl \jour Math. USSR-Sb. \yr 1986 \vol 55 \issue 2 \pages 335--349 \crossref{https://doi.org/10.1070/SM1986v055n02ABEH003008} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Rogachev V., “Subspaces of the Differentiability of Smooth Measures on Infinite-Dimensional Spaces”, 299, no. 1, 1988, 18–22
2. Khafizov M., “On Differentiability Space of Product Measure”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1989, no. 2, 81–84
3. V. I. Bogachev, O. G. Smolyanov, “Analytic properties of infinite-dimensional distributions”, Russian Math. Surveys, 45:3 (1990), 1–104
4. Bogachev V., “Distributions for Analytical Functionals of Random-Processes”, 312, no. 6, 1990, 1291–1296
5. V. I. Bogachev, “Functionals of random processes and infinite-dimensional oscillatory integrals connected with them”, Russian Acad. Sci. Izv. Math., 40:2 (1993), 235–266
6. A. I. Kirillov, “On two mathematical problems of canonical quantization. IV”, Theoret. and Math. Phys., 93:2 (1992), 1251–1261
7. A. I. Kirillov, “Prescription of measures on functional spaces by means of numerical densities and path integrals”, Math. Notes, 53:5 (1993), 555–557
8. A. I. Kirillov, “Infinite-dimensional analysis and quantum theory as semimartingale calculus”, Russian Math. Surveys, 49:3 (1994), 43–95
9. V. I. Bogachev, “Gaussian measures on linear spaces”, Journal of Mathematical Sciences (New York), 79:2 (1996), 933
10. V. I. Bogachev, “Differentiable measures and the Malliavin calculus”, Journal of Mathematical Sciences (New York), 87:4 (1997), 3577
11. V. I. Bogachev, “Measures on topological spaces”, Journal of Mathematical Sciences (New York), 91:4 (1998), 3033
12. Bogachev, VI, “Extensions of H-Lipschitzian mappings with infinite-dimensional range”, Infinite Dimensional Analysis Quantum Probability and Related Topics, 2:3 (1999), 461
13. D. J. Ives, D. Preiss, “Not too well differentiable Lipschitz isomorphisms”, Isr J Math, 115:1 (2000), 343
14. V. I. Bogachev, E. A. Rebrova, “Functions of bounded variation on infinite-dimensional spaces with measures”, Dokl. Math, 87:2 (2013), 144
15. Bogachev V.I., Pilipenko A.Yu., Shaposhnikov A.V., “Sobolev Functions on Infinite-Dimensional Domains”, J. Math. Anal. Appl., 419:2 (2014), 1023–1044
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