Regular Carathéodory-type selectors under no convexity assumptions

We prove the existence of Carathéodory-type selectors (that is, measurable in the first variable and having certain regularity properties like Lipschitz continuity, absolute continuity or bounded variation in the second variable) for multifunctions mapping the product of a measurable space and an interval into compact subsets of a metric space or metric semigroup. © 2005 Elsevier Inc. All rights reserved