Riemann-Stieltjes Integral

• Autorzy: Keiko Narita , Kazuhisa Nakasho , Yasunari Shidama
• Języki publikacji: EN

Abstrakty

EN

In this article, the definitions and basic properties of Riemann-Stieltjes integral are formalized in Mizar [1]. In the first section, we showed the preliminary definition. We proved also some properties of finite sequences of real numbers. In Sec. 2, we defined variation. Using the definition, we also defined bounded variation and total variation, and proved theorems about related properties. In Sec. 3, we defined Riemann-Stieltjes integral. Referring to the way of the article [7], we described the definitions. In the last section, we proved theorems about linearity of Riemann-Stieltjes integral. Because there are two types of linearity in Riemann-Stieltjes integral, we proved linearity in two ways. We showed the proof of theorems based on the description of the article [7]. These formalizations are based on [8], [5], [3], and [4].

Słowa kluczowe

EN

Riemann-Stieltjes integral; bounded variation; linearity

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2016
• Tom: 24
• Numer: 3
• Strony: 199-204

Daty

wydano

2016-09-01

otrzymano

2016-06-30

online

2017-02-08

Twórcy

autor

Keiko Narita

• Hirosaki-city Aomori,

autor

Kazuhisa Nakasho

• Akita Prefectural University Akita,

autor

Yasunari Shidama

• Shinshu University Nagano,

Identyfikatory

DOI

10.1515/forma-2016-0016