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arXiv · 1510.04522

On functions of bounded variation

Christoph Aistleitner·Florian Pausinger·Anne Marie Svane·Robert F. Tichy
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Abstract

The recently introduced concept of $\mathcal{D}$-variation unifies previous concepts of variation of multivariate functions. In this paper, we give an affirmative answer to the open question from Pausinger \& Svane (J. Complexity, 2014) whether every function of bounded Hardy--Krause variation is Borel measurable and has bounded $\mathcal{D}$-variation. Moreover, we show that the space of functions of bounded $\mathcal{D}$-variation can be turned into a commutative Banach algebra.

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Christoph Aistleitner, Florian Pausinger, Anne Marie Svane, Robert F. Tichy. 2015-10-15. On functions of bounded variation. https://arxiv.org/abs/1510.04522

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