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In the present paper we consider the following Satisfaction Problem ofConsumers Demands (SPCD): {\it The supplier must supply the measurable systemof 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 somedynamical system, What is a minimal measure of measurable system which musttake the supplier at the initial time $t=0$ to satisfy demands of all consumers?} In this paper we consider Satisfaction Problem of Consumers Demands measuredby ordinary "Lebesgue measures" in $R^{\infty}$ for various dynamical systemsin $R^{\infty}$. In order to solve this problem we use Liouville type theoremsfor them which describes the dependence between initial and resulting measuresof the entire system.

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