Gauge Integral

• Autorzy: Roland Coghetto
• Języki publikacji: EN

Abstrakty

EN

Some 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.

Słowa kluczowe

EN

Gauge integral; Henstock-Kurzweil integral; generalized Riemann integral

Kategorie tematyczne

• 03B35: Mechanization of proofs and logical operations
• 26A42: Integrals of Riemann, Stieltjes and Lebesgue type
• 26A39: Denjoy and Perron integrals, other special integrals

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2017
• Tom: 25
• Numer: 3
• Strony: 217-225

Daty

wydano

2017-10-01

otrzymano

2017-09-03

online

2017-12-19

Twórcy

autor

Roland Coghetto

• Rue de la Brasserie 5, ,

Identyfikatory

DOI

10.1515/forma-2017-0021