Multi-valued mappings of bounded generalized variation (Q1397325)

The paper deals with some embeddings of function spaces, the structure of the mappings, the jumps of the variation, and the Helly selection principle, among other things. It is shown 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, and 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.