BANACH-ZARETSKY THEOREM FOR COMPACTLY ABSOLUTELY CONTINUOUS MAPPINGS

摘要

For mappings of an interval into locally convex spaces, convex and compact convex analogs of absolute continuity, bounded variation, and the Luzin iV-property are introduced and studied. We prove that, in the general case, a convex analog of the Banach-Zaretsky criteria can be "split" into sufficient and necessary conditions. However, in the Frechet-space case, we have an exact compact analog of the criteria.