Geodesic
On the classification problem of measurable functions in several variables and on matrix distributions
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 22, Tome 441 (2015), pp. 119-143

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We resume the results from [12] on the classification of measurable functions in several variables, with some minor corrections of purely technical nature. We give a partial solution of he characterization problem of so-called matrix distributions, which are the metric invariants of measurable functions introduced in [12]. Matrix distibutions considered as $\S_\mathbb N\times\S_\mathbb N$-invariant, ergodic measures on the space of matrices – this fact connects our problem with Aldous' and Hoover's theorem [2,6]. 
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     author = {A. M. Vershik and U. Hab\"ock},
     title = {On the classification problem of measurable functions in several variables and on matrix distributions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {119--143},
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     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a7/}
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A. M. Vershik; U. Haböck. On the classification problem of measurable functions in several variables and on matrix distributions. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 22, Tome 441 (2015), pp. 119-143. http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a7/