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

• Datum: 2017
• Hauptverfasser: Mikhailets, V. A., Pelekhata, O. B., Михайлець, В. А., Пелехата, Б. Б.
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Інститут математики НАН України 2017
• Online Zugang: https://trim.imath.kiev.ua/index.php/trim/article/view/322
• Назва журналу: 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...