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This article is cited in 1 scientific paper (total in 1 paper)
Classification of measurable functions of several variables and matrix distributions
A. M. Vershikabc a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Saint Petersburg State University
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
Abstract:
We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the
one hand, this is an invariant of this function with respect to a certain group of transformations of variables; on
the other hand, this is a special probability measure in the space of matrices (tensors) that is invariant under
actions of natural infinite permutation groups. The intricate interplay of both interpretations of matrix
(tensor) distributions makes them an important subject of modern functional analysis. We formulate and prove a
theorem that, under certain conditions on a measurable function of two variables,
its matrix distribution is a complete invariant.
Keywords:
classification of functions, matrix distribution, metric triples, pointwise ergodic theorem.
Received: 15.10.2023 Revised: 15.10.2023 Accepted: 20.10.2023
Citation:
A. M. Vershik, “Classification of measurable functions of several variables and matrix distributions”, Funktsional. Anal. i Prilozhen., 57:4 (2023), 46–59; Funct. Anal. Appl., 57:4 (2023), 303–313
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https://www.mathnet.ru/eng/faa4166https://doi.org/10.4213/faa4166 https://www.mathnet.ru/eng/faa/v57/i4/p46
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Abstract page: | 149 | Full-text PDF : | 2 | References: | 27 | First page: | 21 |
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