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Published online by Cambridge University Press: 26 July 2016
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 [20] 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.
Corresponding author: Florian Pausinger, TU Munich, Zentrum Mathematik, M10 Geometrie und Visualisierung, Boltzmannstr. 3, 85748 Garching.