Riemann-Stieltjes Integral

Riemann-Stieltjes Integral

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 a...

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Bibliographic Details
Main Authors: Narita Keiko, Nakasho Kazuhisa, Shidama Yasunari
Format: Article
Language:English
Published: Sciendo 2016-09-01
Series:Formalized Mathematics
Subjects:
26a42
26a45
03b35
riemann-stieltjes integral
bounded variation
linearity
identifier: integr22
version: 8.1.05 5.37.1275
Online Access:https://doi.org/10.1515/forma-2016-0016
Description
Summary: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.
ISSN:1898-9934

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