Satisfaction Problem of Consumers Demands measured by ordinary "Lebesgue measures" in $R^{\infty }$

Abstract

In the present paper we consider the following Satisfaction Problem of Consumers Demands (SPCD): {\it The supplier must supply the measurable system of the measure $m_k$ to the $k$-th consumer at time $t_k$ for $1\le k\le n$. The measure of the supplied measurable system is changed under action of some dynamical system, What is a minimal measure of measurable system which must take the supplier at the initial time $t=0$ to satisfy demands of all consumers ?} In this paper we consider Satisfaction Problem of Consumers Demands measured by ordinary "Lebesgue measures" in $R^{\infty }$ for various dynamical systems in $R^{\infty }$. In order to solve this problem we use Liouville type theorems for them which describes the dependence between initial and resulting measures of the entire system.

13 pages