Relaxed multifunctions and Young multimeasures

Young-measure type limits of multifunctions are examined. The relaxed limit via selections is a multimeasure, while the relaxation as a set-valued point function yields a Young measure on sets. The paper verifies that the two processes are equivalent in the sense that the limit multimeasure consists of all the distributions selectionable with respect to the Young measure on sets. The main tool is the characterization of selectionable distributions. An illustrative application of the equivalence result is provided. Mathematics Subject Classification (1991): 28B20.