“Statistical Physics” or inductive approach to the measure theory and probabilistic and algebraic problems

Kolmogorov's approach to the definition of probability measures in the spaces (using finite-dimensional distributions of the finite sets of functions on the phase space) can be called as the projective approach. But there is an dual or inductive approach to the definition of measures on the phase space — when a measure is defined using a partition of the phase space, more exactly, on the layers of the partition. This leads to the generalization of the remarkable theory of Rokhlin's — theory of the measurable partitions (40-th). The necessity of the generalization of Kolmogorov theory from a practical point of view had appeared in 60-th in statistical physics and theory of Markov processes. (due to Dobrushin and Dynkin). In the last period this necessity became actual because of the series of new problems of the theory of representation asymptotic combinatorics. The speaker is supposed to excite the interest of the audience with this new topic which has the theoretical as well as practical senses. No special knowledge is necessary to understand the talk.