The recently introduced concept of D-variation unifies previous concepts of variation of multivariate functions. In this paper, we give an affirmative answer to the open question from  whether every function of bounded Hardy-Krause variation is Borel measurable and has bounded D-variation. Moreover, we show that the space of functions of bounded D-variation can be turned into a commutative Banach algebra.
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|Early online date||26 Jul 2017|
|Publication status||Early online date - 26 Jul 2017|
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