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Title: Gauge-measurable functions
Authors: Ponce, Augusto C.
Van Schaftingen, Jean
Keywords: gauge integralKurzweil-Henstock integralLebesgue integralgeneralized Riemann integralmeasurable functiongauge
Issue Date: 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
Journal: Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics 
Part of: 49 (2017)
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.
Type: Article
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/2464-8728/16208
Rights: Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Appears in Collections:Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.49 (2017)

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