CONTINUITY OF SINGLE- AND MULTIVALUED SUPERPOSITION OPERATORS IN GENERALIZED IDEAL SPACES OF MEASURABLE VECTOR FUNCTIONS

Abstract

A generalization of ideal spaces of measurable vector functions is introduced. A Vitali convergence theorem for sets is proved in these spaces. It is proved that for superposition operators the acting condition in such spaces implies the continuity. Also analogous statements for upper and lower semicontinuous multivalued maps are obtained.