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On functions of bounded variation

  • CHRISTOPH AISTLEITNER (a1), FLORIAN PAUSINGER (a2), ANNE MARIE SVANE (a3) and ROBERT F. TICHY (a4)
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 [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.

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Corresponding author: Florian Pausinger, TU Munich, Zentrum Mathematik, M10 Geometrie und Visualisierung, Boltzmannstr. 3, 85748 Garching.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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