Pointwise limits of continuous monotone functions and functions of bounded variation

Maslyuchenko Volodymyr Kyrylovych; Petey Stepan Pavlovych

Maslyuchenko Volodymyr Kyrylovych ¹ , Petey Stepan Pavlovych ¹

¹ Department of Mathematical Analysis, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

Keywords: рointwise limits, continuous monotone functions, functions of limited variation

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Abstract

An analog of Hahn`s insertion theorem is proven. With its help we obtain that every increasing function $f : [a;b] → \mathbb{R}$ is the pointwise limit of a sequence of increasing continuous functions $f_n : [a;b] → \mathbb{R}$.

References

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ACS Style: Maslyuchenko, V.K.; Petey, S.P. Pointwise limits of continuous monotone functions and functions of bounded variation. Bukovinian Mathematical Journal. 2016, 3
AMA Style: Maslyuchenko VK, Petey SP. Pointwise limits of continuous monotone functions and functions of bounded variation. Bukovinian Mathematical Journal. 2016; 3(2).
Chicago/Turabian Style: Volodymyr Kyrylovych Maslyuchenko, Stepan Pavlovych Petey. 2016. "Pointwise limits of continuous monotone functions and functions of bounded variation". Bukovinian Mathematical Journal. 3 no. 2.

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