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http://hdl.handle.net/10077/16208| Title: | Gauge-measurable functions | Authors: | Ponce, Augusto C. Van Schaftingen, Jean |
Keywords: | gauge integral; Kurzweil-Henstock integral; Lebesgue integral; generalized Riemann integral; measurable function; gauge | 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) | 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. | URI: | http://hdl.handle.net/10077/16208 | 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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| File | Description | Size | Format | |
|---|---|---|---|---|
| 08_RIMUT_PonceVan.pdf | 360.25 kB | Adobe PDF | View/Open |
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