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.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 403, 2012, pp. 35–57.
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Vershik, A.M. On classification of measurable functions of several variables. J Math Sci 190, 427–437 (2013). https://doi.org/10.1007/s10958-013-1258-0
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DOI: https://doi.org/10.1007/s10958-013-1258-0