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

• Date: 2017
• Author Affiliations: В. А. Михайлець — Інститут математики НАН України; Б. Б. Пелехата — Нацiональний технiчний унiверситет України "КПI"
• Keywords: keywords
• Main Authors: Mikhailets, V. A., Pelekhata, O. B., Михайлець, В. А., Пелехата, Б. Б.
• Format: Article
• Language: Ukrainian
• Published: Інститут математики НАН України 2017
• Online Access: https://trim.imath.kiev.ua/index.php/trim/article/view/322
• Journal Title: Transactions of Institute of Mathematics of NAS of Ukraine

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 th...