REPOZYTORIUM UNIWERSYTETU
W BIAŁYMSTOKU

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 Tytuł: Gauge Integral Autorzy: Coghetto, Roland Słowa kluczowe: Gauge integralHenstock-Kurzweil integralgeneralized Riemann integral Data wydania: 2017 Data dodania: 8-lut-2018 Wydawca: DeGruyter Open Źródło: Formalized Mathematics, Volume 25, Issue 3, Pages 217–225 Abstrakt: SummarySome authors have formalized the integral in the Mizar Mathematical Library (MML). The first article in a series on the Darboux/Riemann integral was written by Noboru Endou and Artur Korniłowicz: [6]. The Lebesgue integral was formalized a little later [13] and recently the integral of Riemann-Stieltjes was introduced in the MML by Keiko Narita, Kazuhisa Nakasho and Yasunari Shidama [12].A presentation of definitions of integrals in other proof assistants or proof checkers (ACL2, COQ, Isabelle/HOL, HOL4, HOL Light, PVS, ProofPower) may be found in [10] and [4].Using the Mizar system [1], we define the Gauge integral (Henstock-Kurzweil) of a real-valued function on a real interval [a, b] (see [2], [3], [15], [14], [11]). In the next section we formalize that the Henstock-Kurzweil integral is linear.In the last section, we verified that a real-valued bounded integrable (in sense Darboux/Riemann [6, 7, 8]) function over a interval a, b is Gauge integrable.Note that, in accordance with the possibilities of the MML [9], we reuse a large part of demonstrations already present in another article. Instead of rewriting the proof already contained in [7] (MML Version: 5.42.1290), we slightly modified this article in order to use directly the expected results. Afiliacja: Rue de la Brasserie 5, 7100 La Louvière, Belgium URI: http://hdl.handle.net/11320/6296 DOI: 10.1515/forma-2017-0021 ISSN: 1426-2630 e-ISSN: 1898-9934 Typ Dokumentu: Article Występuje w kolekcji(ach): Formalized Mathematics, 2017, Volume 25, Issue 3

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