Geodesic
On classification of measurable functions of several variables
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXI, Tome 403 (2012), pp. 35-57

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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 its invariants (the system of joint distributions), and relate these notions to matrix distributions, i.e., another invariant of measurable functions, which was found earlier and is a random matrix. 
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     author = {A. M. Vershik},
     title = {On classification of measurable functions of several variables},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_403_a2/}
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A. M. Vershik. On classification of measurable functions of several variables. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXI, Tome 403 (2012), pp. 35-57. http://geodesic.mathdoc.fr/item/ZNSL_2012_403_a2/