On the classification problem of matrix distributions of measurable functions in several variables

A. Vershik; U. Haböck

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arXiv · 1512.06760

On the classification problem of matrix distributions of measurable functions in several variables

A. Vershik·U. Haböck

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Abstract

We resume the results from \cite{Vershik FA} on the classification of measurable functions in several variables, with some minor corrections of purely technical nature, and give a partial solution to the characterization problem of so--called matrix distributions, which are the metric invariants of measurable functions introduced in \cite{Vershik FA}. The characterization of these invariants of the ergodic measures on the space of matrices is closely related to Aldous' and Hoover's representation of row-- and column--exchangable distributions \cite{Aldous1981,Hoover1982}, but not in such an obvious way as was initially expected in \cite{Vershik FA}.

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A. Vershik, U. Haböck. 2015-12-17. On the classification problem of matrix distributions of measurable functions in several variables. https://arxiv.org/abs/1512.06760

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