Theorem of conflicts for a pair of probability measures

Abstract.

We develop mathematical tools suitable for the construction of conflict models with non-annihilating adversaries. In a set of probability measures we introduce a non-commutative conflict composition and consider the associated dynamical system. We prove that for each couple of non-identical mutually nonsingular measures, the corresponding trajectory of the dynamical system converges to an invariant point represented by a pair of mutually singular measures. The disjoint supports of the limiting measures determine the final re-distribution of the starting area of conflict as a result of an “infinite war” for existence space (the pure repelling effect).