A Generalization of Reisz characterization of absolute continuity in Lp a,b−spaces

We initiate studies of a new classical characterization of absolute continuity which promises to be invaluable in studies and further generalizations of nonclassical characterizations of absolute continuity in diversely more general function spaces. Our main objective is showing that our newer characterization for absolute continuity includes Riesz characterization in Lp−spaces (p>1) by allowing the situation p≥ 1. Our method also enriches studies of connection between absolute continuity and rapidly Cauchy sequences.