On essential absolute continuity
Robert J. Thompson · Pacific Journal of Mathematics · 1961
Throughout this paper D will denote a bounded domain in Euclidean w-space R n , and T will be a bounded, continuous, single-valued transformation from D into R n .For such transformations, concepts of essential bounded variation and essential absolute continuity have been defined and studied by Rado and Reichelderfer ([3], IV. 4).In this paper a characterization of essential absolute continuity will be given.The characterization suggests a definition of uniform essential absolute continuity and some of the consequences of this definition will be investigated.