Criterions for absolute continuity on time scales

Abstract

Abstract In this paper, we establish the concept of absolutely continuous function on and we prove a characterization of such functions, which generalizes the one given for the real case in the classical Banach-Zarecki Theorem. Moreover, we prove that this kind of functions satisfy the Fundamental Theorem of Calculus. A criterion for absolute continuity of the inverse function of any strictly monotone and absolutely continuous function on is also obtained. †Research partially supported by D. G. I. and F.E.D.E.R. project BFM2001-3884-C02-01, and by Xunta of Galicia and F.E.D.E.R. project PGIDIT020XIC20703PN, Spain. Keywords: Absolute continuous functionsTime scales calculusΔ-integralΔ-measure39A10 Notes †Research partially supported by D. G. I. and F.E.D.E.R. project BFM2001-3884-C02-01, and by Xunta of Galicia and F.E.D.E.R. project PGIDIT020XIC20703PN, Spain. [e-mail]