ABSOLUTELY CONTINUOUS FUNCTIONS & FUNCTIONS OF BOUNDED VARIATION

The study of Absolutely continuous functions and functions of bounded variation on an interval [ a, b ] is a part of study of a good M.Sc. course in Real Analysis, so the properties are well known. A less well known fact is that BV[a, b], the collection of all functions of bounded variation on [a, b] is a Banach algebra. This book is my M.Phil. dissertation, which was carried out under the guidance of Prof. R.D. Mehta, Department of Mathematics, S.P. University, Vallabh Vidyanagar. It is about the generalization of definitions of functions of bounded variation and absolutely continuous functions on any compact subset of real numbers as well as on product of two closed intervals and then it is shown that they are Banach algebras with certain norms.