A. G. Chentsov
An abstract version of the programmed iteration method used in the differential games (DG) theory is considered. The problem of the existence of non-anticipating set-valued selectors (SVS) of an "arbitrary" set-valued mapping (SVM) is investigated. The operator realizing by its powers the transfer of a priori SVM in the greatest non-anticipating SVS of the given SVM is constructed. In terms of universal (in the given class of operators) fixed points, the representation of non-anticipating SVS is established. In terms of a natural factor space connected with the mapping, germs having the sense of noise realizations in the DG theory and the localization of basic properties of non-anticipating SVM are constructed.