Journal of Mathematical Sciences

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

On classification of measurable functions of several variables

  • A. M. Vershik

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.


Normal Form Measurable Function Joint Distribution Random Matrix Complete System 
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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. 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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