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Article 20

The decomposition of a VB* function

An. St. Univ. Ovidius Constanta, 1 (1995)

Mathematical reviews subject classification: 26A45.

 

Abstract

It is well known the following result on functions with bounded variation:

         
If F:[a,b] → R is VB on a subset P of [a,b], then F is the difference of two increasing functions on P.

(see S. Saks, Theory of the integral, 2nd. rev. ed., vol. PWN, Monografie  Matematyczne, Warsaw, 1937).
         

In the present paper we show that this result remains true if VB and increasing are replaced by VB* and increasing*.