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

This article is cited in 15 scientific papers (total in 15 papers)

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
Received: 19.05.1983 and 15.06.1984

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
\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
\jour Math. USSR-Sb.
\yr 1986
\vol 55
\issue 2
\pages 335--349

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    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  mathscinet  isi
    2. Khafizov M., “On Differentiability Space of Product Measure”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1989, no. 2, 81–84  mathscinet  zmath  isi
    3. V. I. Bogachev, O. G. Smolyanov, “Analytic properties of infinite-dimensional distributions”, Russian Math. Surveys, 45:3 (1990), 1–104  mathnet  crossref  mathscinet  zmath  isi
    4. Bogachev V., “Distributions for Analytical Functionals of Random-Processes”, 312, no. 6, 1990, 1291–1296  mathscinet  zmath  isi
    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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. A. I. Kirillov, “On two mathematical problems of canonical quantization. IV”, Theoret. and Math. Phys., 93:2 (1992), 1251–1261  mathnet  crossref  mathscinet  isi
    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  mathnet  crossref  mathscinet  zmath  isi  elib
    8. A. I. Kirillov, “Infinite-dimensional analysis and quantum theory as semimartingale calculus”, Russian Math. Surveys, 49:3 (1994), 43–95  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. V. I. Bogachev, “Gaussian measures on linear spaces”, Journal of Mathematical Sciences (New York), 79:2 (1996), 933  crossref  mathscinet  zmath
    10. V. I. Bogachev, “Differentiable measures and the Malliavin calculus”, Journal of Mathematical Sciences (New York), 87:4 (1997), 3577  crossref  mathscinet  zmath
    11. V. I. Bogachev, “Measures on topological spaces”, Journal of Mathematical Sciences (New York), 91:4 (1998), 3033  crossref  mathscinet  zmath
    12. Bogachev, VI, “Extensions of H-Lipschitzian mappings with infinite-dimensional range”, Infinite Dimensional Analysis Quantum Probability and Related Topics, 2:3 (1999), 461  crossref  isi
    13. D. J. Ives, D. Preiss, “Not too well differentiable Lipschitz isomorphisms”, Isr J Math, 115:1 (2000), 343  crossref  mathscinet  zmath  isi
    14. V. I. Bogachev, E. A. Rebrova, “Functions of bounded variation on infinite-dimensional spaces with measures”, Dokl. Math, 87:2 (2013), 144  crossref
    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  crossref  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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