Invariant and quasiinvariant measures in infinite-dimensional topological vector spaces

By Gogi Pantsulaia

Subjects: Probabiities, Measure theory, Stochastic processes, Real analysis, Vector spaces, Invariant measures, Ergodic theory, Mathematical statistics

Description: This monograph deals with certain aspects of the general theory of systems. The author develops the ergodic theory (i.e.), the theory of quaslinvariant and invariant measures) in such infinite-dimensional vector spaces which appear as models of various (physical, economic, genetic, linquistic, social, etc.)processes. The methods of ergodic theory are sucessful as applied to study properties of such systems. A foundation for ergodic theory was stimulated by the necessity of a consideration of statistic mechanic problems and was directly connected with the works of G. Birkhoff, Kryloff and Bogoliuboff, E. Hoph and other famous mathematicians.