Banach--Zaretsky theorem for compactly absolutely continuous mappings

I. V. Orlov

Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 37 (2010), pp. 38-54

Résumé

For mappings of an interval into locally convex spaces, convex and compact convex analogs of absolute continuity, bounded variation, and the Luzin $N$-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 Fréchet-space case, we have an exact compact analog of the criteria.