On classification of measurable functions of several variables. (English. Russian original) Zbl 1388.28003
J. Math. Sci., New York 190, No. 3, 427-437 (2013); translation from Zap. Nauchn. Semin. POMI 403, 35-57 (2012).
Summary: 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.
MSC:
| 28A20 | Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence |
| 60B20 | Random matrices (probabilistic aspects) |
References:
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| [6] | A. Vershik and U. Haböck, ”Compactness of the congruence group of measurable functions in several variables,” J. Math. Sci. (N. Y.), 141, No. 6, 1601–1607 (2007). · doi:10.1007/s10958-007-0068-7 |
| [7] | A. Vershik and U. Haböck, ”Canonical model of measurable functions of two variables with given matrix distributions,” Manuscript, Vienna (2005). |
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