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Mat. Sb. (N.S.), 1949, Volume 25(67), Number 1, Pages 107–150 (Mi msb5995)  

This article is cited in 43 scientific papers (total in 44 papers)

On the fundamental ideas of measure theory

V. A. Rokhlin


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Received: 15.07.1947

Citation: V. A. Rokhlin, “On the fundamental ideas of measure theory”, Mat. Sb. (N.S.), 25(67):1 (1949), 107–150

Citation in format AMSBIB
\Bibitem{Rok49}
\by V.~A.~Rokhlin
\paper On the fundamental ideas of measure theory
\jour Mat. Sb. (N.S.)
\yr 1949
\vol 25(67)
\issue 1
\pages 107--150
\mathnet{http://mi.mathnet.ru/msb5995}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=30584}
\zmath{https://zbmath.org/?q=an:0033.16904}


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    This publication is cited in the following articles:
    1. V. A. Rokhlin, “Lectures on the entropy theory of measure-preserving transformations”, Russian Math. Surveys, 22:5 (1967), 1–52  mathnet  crossref  mathscinet  zmath
    2. D. V. Anosov, Ya. G. Sinai, “Some smooth ergodic systems”, Russian Math. Surveys, 22:5 (1967), 103–167  mathnet  crossref  mathscinet  zmath
    3. A. D. Ioffe, V. M. Tikhomirov, “Duality of convex functions and extremum problems”, Russian Math. Surveys, 23:6 (1968), 53–124  mathnet  crossref  mathscinet  zmath
    4. A. B. Katok, A. M. Stepin, “Metric properties of measure preserving homeomorphisms”, Russian Math. Surveys, 25:2 (1970), 191–220  mathnet  crossref  mathscinet  zmath
    5. E. I. Dinaburg, “On the relations among various entropy characteristics of dynamical systems”, Math. USSR-Izv., 5:2 (1971), 337–378  mathnet  crossref  mathscinet  zmath
    6. V. Ya. Golodets, “Crossed products of von Neumann algebras”, Russian Math. Surveys, 26:5 (1971), 1–50  mathnet  crossref  mathscinet  zmath
    7. V. G. Sharapov, “Markov endomorphisms of Lebesgue space”, Funct. Anal. Appl., 5:3 (1971), 246–249  mathnet  crossref  mathscinet  zmath
    8. L. A. Bunimovich, “On a class of special flows”, Math. USSR-Izv., 8:1 (1974), 219–232  mathnet  crossref  mathscinet  zmath
    9. V. L. Levin, “Convex integral functionals and the theory of lifting”, Russian Math. Surveys, 30:2 (1975), 119–184  mathnet  crossref  mathscinet  zmath
    10. A. M. Vershik, I. M. Gel'fand, M. I. Graev, “Representations of the group of diffeomorphisms”, Russian Math. Surveys, 30:6 (1975), 1–50  mathnet  crossref  mathscinet  zmath
    11. T. V. Volkova, “O maksimalnykh kommutativnykh regulyarnykh podalgebrakh v faktore tipa II$_1$”, UMN, 30:6(186) (1975), 163–164  mathnet  mathscinet  zmath
    12. V. Ya. Golodets, “Reduction of type III algebras”, Funct. Anal. Appl., 9:4 (1975), 273–278  mathnet  crossref  mathscinet  zmath
    13. V. S. Klimov, “Imbedding theorems and geometric inequalities”, Math. USSR-Izv., 10:3 (1976), 615–638  mathnet  crossref  mathscinet  zmath
    14. M. P. Ershov, “K teoreme Rokhlina o nezavisimom dopolnenii”, UMN, 32:1(193) (1977), 187–188  mathnet  mathscinet  zmath
    15. Ya. B. Pesin, “Characteristic Lyapunov exponents and smooth ergodic theory”, Russian Math. Surveys, 32:4 (1977), 55–114  mathnet  crossref  mathscinet  zmath
    16. V. G. Vinokurov, N. N. Ganikhodzhaev, “Conditional functions in the trajectory theory of dynamical systems”, Math. USSR-Izv., 13:2 (1979), 221–252  mathnet  crossref  mathscinet  zmath  isi
    17. M. Sh. Birman, A. M. Vershik, M. Z. Solomyak, “Product of commuting spectral measures need not be countably additive”, Funct. Anal. Appl., 13:1 (1979), 48–49  mathnet  crossref  mathscinet  zmath
    18. A. L. Fëdorov, “Polymorphisms and partitions of Lebesgue spaces”, Funct. Anal. Appl., 16:2 (1982), 150–152  mathnet  crossref  mathscinet  zmath  isi
    19. V. G. Vinokurov, A. N. Fozilov, “Classification of pairs of discrete measurable partitions of the Lebesgue space”, Russian Math. Surveys, 41:2 (1986), 221–222  mathnet  crossref  mathscinet  zmath  isi
    20. M. Yu. Lyubich, “The dynamics of rational transforms: the topological picture”, Russian Math. Surveys, 41:4 (1986), 43–117  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    21. A. M. Vershik, “The universal Urysohn space, Gromov metric triples and random metrics on the natural numbers”, Russian Math. Surveys, 53:5 (1998), 921–928  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    22. I. V. Nepomnyaschih, A. V. Ponosov, “Local operators in some subspaces of the space $L_0$”, Russian Math. (Iz. VUZ), 43:6 (1999), 48–61  mathnet  mathscinet  zmath  elib
    23. S. S. Gabrielyan, “On Projective Mappings”, Math. Notes, 72:3 (2002), 295–300  mathnet  crossref  crossref  mathscinet  zmath  isi
    24. A. V. Chistyakov, “On piecewise-injective measurable mappings”, Russian Math. (Iz. VUZ), 50:5 (2006), 62–66  mathnet  mathscinet  zmath  elib
    25. S. V. Tikhonov, “A complete metric in the set of mixing transformations”, Sb. Math., 198:4 (2007), 575–596  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    26. A. G. Kachurovskii, “General Theories Unifying Ergodic Averages and Martingales”, Proc. Steklov Inst. Math., 256 (2007), 160–187  mathnet  crossref  mathscinet  zmath  elib  elib
    27. A. M. Vershik, A. D. Gorbul'skii, “Scaled entropy of filtrations of $\sigma$-fields”, Theory Probab. Appl., 52:3 (2008), 493–508  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    28. V. N. Sudakov, “Weizsäcker phenomenon and Gaussian Lebesgue–Rokhlin space”, J. Math. Sci. (N. Y.), 163:4 (2010), 430–445  mathnet  crossref  elib
    29. Chistyakov A.V., “Silnaya neobratimost operatorov sdviga vdol traektorii brounovskogo dvizheniya”, Vestn. Permskogo un-ta. Ser.: Matem. Mekh. Inform., 2009, no. 7, 84–89  elib
    30. A. M. Levin, “Decomposability of polymorphisms generated by an action of two finite groups”, J. Math. Sci. (N. Y.), 174:1 (2011), 23–27  mathnet  crossref
    31. I. V. Podvigin, “A martingale ergodic theorem”, Siberian Math. J., 51:6 (2010), 1125–1130  mathnet  crossref  mathscinet  isi  elib
    32. A. M. Vershik, “Scailing entropy and automorphisms with pure pointspectrum”, St. Petersburg Math. J., 23:1 (2012), 75–91  mathnet  crossref  mathscinet  zmath  isi  elib
    33. R. I. Grigorchuk, “Some topics in the dynamics of group actions on rooted trees”, Proc. Steklov Inst. Math., 273 (2011), 64–175  mathnet  crossref  mathscinet  zmath  isi  elib
    34. Lasanen S., “Non-Gaussian Statistical Inverse Problems. Part I: Posterior Distributions”, Inverse Probl. Imaging, 6:2 (2012), 215–266  crossref  isi
    35. Yu. A. Neretin, “On the boundary of the group of transformations leaving a measure quasi-invariant”, Sb. Math., 204:8 (2013), 1161–1194  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    36. A. I. Bufetov, “Ergodic decomposition for measures quasi-invariant under a Borel action of an inductively compact group”, Sb. Math., 205:2 (2014), 192–219  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    37. Yu. A. Neretin, “Bi-invariant functions on the group of transformations leaving a measure quasi-invariant”, Sb. Math., 205:9 (2014), 1357–1372  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    38. A. M. Vershik, P. B. Zatitskiy, F. V. Petrov, “Virtual continuity of measurable functions and its applications”, Russian Math. Surveys, 69:6 (2014), 1031–1063  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    39. J. Math. Sci. (N. Y.), 209:6 (2015), 826–829  mathnet  crossref
    40. P. B. Zatitskiy, “Scaling entropy sequence: invariance and examples”, J. Math. Sci. (N. Y.), 209:6 (2015), 890–909  mathnet  crossref
    41. A. V. Alpeev, “Announce of an entropy formula for a class of Gibbs measures”, J. Math. Sci. (N. Y.), 224:2 (2017), 171–175  mathnet  crossref  mathscinet
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    43. H. V. Weizsäcker, “A few recollections”, Veroyatnost i statistika. 25, Posvyaschaetsya pamyati Vladimira Nikolaevicha SUDAKOVA, Zap. nauchn. sem. POMI, 457, POMI, SPb., 2017, 9–11  mathnet
    44. A. M. Vershik, “Dvoistvennost i svobodnye mery v vektornykh prostranstvakh, spektralnaya teoriya deistvii ne lokalno kompaktnykh grupp”, Veroyatnost i statistika. 25, Posvyaschaetsya pamyati Vladimira Nikolaevicha SUDAKOVA, Zap. nauchn. sem. POMI, 457, POMI, SPb., 2017, 74–100  mathnet
  • Математический сборник (новая серия) - 1947–1963
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