On approximation of functions from tne class $NBV[a,b]$

Abstract

We prove that each function from $NBV[a,b]$ is a uniform limit of step functions of the same class, such that their marginal steps may degenerate into points and their variations are collectively bounded. In particular this yields linear span of Dirac $\delta$-measures to be sequentially dense in the space of Radon measures on $[a,b]$ in $w^*$-topology.