On the Classification Problem of Measurable Functions in Several Variables and on Matrix Distributions

Аннотация

We resume results of the first author on classification of measurable functions in several variables, with some minor corrections of purely technical nature. We give a partial solution of the characterization problem for so-called matrix distributions which are metric invariants of measurable functions introduced by the first author. Matrix distributions are considered as (S_ℕ × S_ℕ)-invariant, ergodic measures on the space of matrices; this fact connects our problem with Aldous’ and Hoover’s theorem. Bibliography: 14 titles.