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arXiv · 1510.06251

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

Gogi Pantsulaia·Givi Giorgadze
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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.

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Gogi Pantsulaia, Givi Giorgadze. 2016-12-17. Satisfaction Problem of Consumers Demands measured by ordinary "Lebesgue measures" in $R^{\infty}$. https://doi.org/10.13140/rg.2.1.1044.0404

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