This article is cited in 19 papers

Multi-Valued Mappings of Bounded Generalized Variation

V. V. Chistyakov

N. I. Lobachevski State University of Nizhni Novgorod

Abstract: We study the mappings taking real intervals into metric spaces and possessing a bounded generalized variation in the sense of Jordan–Riesz–Orlicz. We establish some embeddings of function spaces, the structure of the mappings, the jumps of the variation, and the Helly selection principle. We show that a compact-valued multi-valued mapping of bounded generalized variation with respect to the Hausdorff metric has a regular selection of bounded generalized variation. We prove the existence of selections preserving the properties of multi-valued mappings that are defined on the direct product of an interval and a topological space, have a bounded generalized variation in the first variable, and are upper semicontinuous in the second variable.

UDC: 517.518.24+515.124

Received: 02.02.2000
Revised: 09.02.2001

DOI: 10.4213/mzm372

 English version: Mathematical Notes, 2002, 71:4, 556–575

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