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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year

SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

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Volume 24, Issue 4


The Basic Existence Theorem of Riemann-Stieltjes Integral

Kazuhisa Nakasho / Keiko Narita / Yasunari Shidama
Published Online: 2017-02-23 | DOI: https://doi.org/10.1515/forma-2016-0021


In this article, the basic existence theorem of Riemann-Stieltjes integral is formalized. This theorem states that if f is a continuous function and ρ is a function of bounded variation in a closed interval of real line, f is Riemann-Stieltjes integrable with respect to ρ. In the first section, basic properties of real finite sequences are formalized as preliminaries. In the second section, we formalized the existence theorem of the Riemann-Stieltjes integral. These formalizations are based on [15], [12], [10], and [11].

Keywords: Riemann-Stieltjes integral; bounded variation; continuous function

MSC 2010: 26A42; 26A45; 03B35


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About the article

Received: 2016-10-18

Published Online: 2017-02-23

Published in Print: 2016-12-01

Citation Information: Formalized Mathematics, Volume 24, Issue 4, Pages 253–259, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.1515/forma-2016-0021.

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© 2016 Kazuhisa Nakasho et al., published by De Gruyter Open. This work is licensed under version 3.0 of the Creative Commons Attribution–ShareAlike License. BY-SA 3.0

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