Absolutely continuous variational measures of Mawhin’s type

Abstract

ABSTRACT. In this paper we study absolutely continuous and σ-finite variational measures corresponding to Mawhin, F -and BV -integrals. We obtain characterization of these σ-finite variational measures similar to those obtained in the case of standard variational measures. We also give a new proof of the Radon-Nikodým theorem for these measures.

A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting

“…We refer to the elements β of B as basis sets. Some particular examples of derivation basis in different types of topological spaces can be found in [2,16,24,29,30,34].…”