Theorem of conflicts for a pair of probability measures (Q1762678)

This paper provides mathematical tools suitable for the construction of conflict models with non-annihilating adversaries, and also introduces a non-commutative conflict composition in a set of probability measures and then deals with the associated dynamical system. It is proved 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 the existence space.