Classification of the Measurable Functions of Several Arguments and Invariant Measures on the Space of Matrices and Tensors

Classification of the measurable functions of several arguments and invariant measures on the space of matrices and tensors, 1. Classificaton. Content 1.Introduction: list of the problems. 2.Classificaton of measurable functions:one variable and pure functions. 2.1.Classical case-functions of one variable. 2.2.Pure functions. 3.Complete metric invariant of the measurable functions of several arguments: matrix distribution. 3.1. Definition of matrix distribution. 3.2. Complete invariant in the Probelm (F). 3.3.Symmetries. 4.Properties of matrix distributions as a invariant measures on the space of matrices. 4.1.Distributions of the columns and rows. 4.2.Matrix distribution is a simple measure in the space M N (R). 4.3 Additional properties of the distributions of the columns and rows, and final remarks. References.