Properties of functions of generalized bounded variation

Abstract

The class of functions of $\Lambda BV^{(p)}$ shares manyproperties of functions of bounded variation. Here we have shownthat $\Lambda BV^{(p)}$ is a Banach space with a suitable norm,the intersection of $\Lambda BV^{(p)}$, over all sequences$\Lambda$, is the class of functions of BV$^{(p)}$ and the unionof $\Lambda BV^{(p)}$, over all sequences $\Lambda$, is theclass of functions having right- and left-hand limits at every point.