A Banach algebra of functions of several variables of finite total variation and Lipschitzian superposition operators. II

We characterize superposition Nemytskii operators, which map the Banach algebra of functions of n real variables with finite total variation in the sense of Vitali, Hardy and Krause into itself and satisfy the global Lipschitz condition. Our results extend previous results in this direction by Matkowski and Mis in [Math. Nachr. 117 (1984) 155-159] for n = 1 and the author in [Monatsh. Math. 137(2) (2002) 99-114] for n = 2. (c) 2005 Elsevier Ltd. All rights reserved

Regular Caratheodory-type selectors under no convexity assumptions

We prove the existence of Caratheodory-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. (c) 2005 Elsevier Inc. All rights reserved