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Journal of Mathematical Sciences

, Volume 190, Issue 3, pp 427–437 | Cite as

On classification of measurable functions of several variables

  • A. M. Vershik
Article

We define a normal form (called the canonical image) of an arbitrary measurable function of several variables with respect to a natural group of transformations; describe a new complete system of invariants of such a function (the system of joint distributions); and relate these notions to the matrix distribution, another invariant of measurable functions found earlier, which is a random matrix. Bibliography: 7 titles.

Keywords

Normal Form Measurable Function Joint Distribution Random Matrix Complete System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    M. Gromov, Metric Structures for Riemannian and non-Riemannian Spaces, Birkhäuser Boston, Boston (2001).Google Scholar
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    V. A. Rokhlin, “Metric classification of measurable functions,” Uspekhi Mat. Nauk, 12, No. 2(74), 169–174 (1957).MATHGoogle Scholar
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    A. M. Vershik, “Decription on invariant measures for the actions of some infinite-dimensional groups,” Sov. Math. Dok., 15, 1396–1400 (1974).MATHGoogle Scholar
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    A. M. Vershik, “Classification of measurable functions of several arguments, and invariantly distributed random matrices,” Funct. Anal. Appl., 36, No. 2, 93–105 (2002).MathSciNetMATHCrossRefGoogle Scholar
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    A. M. Vershik, “Random metric spaces and universality,” Russian Math. Surveys, 59, No. 2, 259–295 (2004).MathSciNetCrossRefGoogle Scholar
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    A. Vershik and U. Haböck, “Compactness of the congruence group of measurable functions in several variables,” J. Math. Sci. (N. Y.), 141, No. 6, 1601–1607 (2007).MathSciNetCrossRefGoogle Scholar
  7. 7.
    A. Vershik and U. Haböck, “Canonical model of measurable functions of two variables with given matrix distributions,” Manuscript, Vienna (2005).Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.St. Petersburg Department of Steklov Mathematical InstituteSt. PetersburgRussia

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