Hahn-Jordan decomposition as an equilibrium state of the conflict system

Abstract

The notion of conflict system is introduced in terms of couples of probability measures. We construct several models of conflict systems and show that every trajectory with initial state given by a couple of measures $\mu, \nu$ converges to an equilibrium state specified by the normalized components $\mu_+, \nu_+$ of the classical Hahn – Jordan decomposition of the signed measure $\omega = \mu - \nu$.