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Gauge-measurable functions
Ponce, Augusto C.
Van Schaftingen, Jean
2017
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e-ISSN
2464-8728
Abstract
In 1973, E. J. McShane introduced an alternative definition of the Lebesgue integral based on Riemann sums, where gauges are used to decide what tagged partitions are allowed. Such an approach does not require any preliminary knowledge of Measure Theory. We investigate in this paper a definition of measurable functions also based on gauges. Its relation to the gauge-integrable functions that satisfy McShane’s definition is obtained using elementary tools from Real Analysis. We show in particular a dominated integration property of gauge-measurable functions.
Part of
49 (2017)
Publisher
EUT Edizioni Università di Trieste
Source
Augusto C. Ponce, Jean Van Schaftingen, "Gauge-measurable functions", in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics", 49 (2017), Trieste, EUT Edizioni Università di Trieste, 2017, pp. 113-135
Languages
en
Rights
Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
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