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

• Дата: 2017
• Автори: Mikhailets, V. A., Pelekhata, O. B., Михайлець, В. А., Пелехата, Б. Б.
• Формат: Стаття
• Мова: Українська
• Опубліковано: Інститут математики НАН України 2017
• Онлайн доступ: 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...