On the Riemann-Stieltjes Integral
This study contributes to the theory of Riemann-Stieltjes integral. We prove that if all continuous piecewise linear functions are Riemann-Stieltjes integrable with respect to a bounded integrator α : [a,b] → R, then α must be of bounded variation on [a,b]. We also provide some other consequences....
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| Format: | Article |
| Language: | English |
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University of Kashan
2022-06-01
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| Series: | Mathematics Interdisciplinary Research |
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| Online Access: | https://mir.kashanu.ac.ir/article_111967_38e1e40e7615202c24ada1b09fba3a91.pdf |
| _version_ | 1797630820306911232 |
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| author | Ali Parsian |
| author_facet | Ali Parsian |
| author_sort | Ali Parsian |
| collection | DOAJ |
| description | This study contributes to the theory of Riemann-Stieltjes integral. We prove that if all continuous piecewise linear functions are Riemann-Stieltjes integrable with respect to a bounded integrator α : [a,b] → R, then α must be of bounded variation on [a,b]. We also provide some other consequences. |
| first_indexed | 2024-03-11T11:13:11Z |
| format | Article |
| id | doaj.art-24cf454fea154732afe39efd4ad5770a |
| institution | Directory Open Access Journal |
| issn | 2476-4965 |
| language | English |
| last_indexed | 2024-03-11T11:13:11Z |
| publishDate | 2022-06-01 |
| publisher | University of Kashan |
| record_format | Article |
| series | Mathematics Interdisciplinary Research |
| spelling | doaj.art-24cf454fea154732afe39efd4ad5770a2023-11-11T10:05:52ZengUniversity of KashanMathematics Interdisciplinary Research2476-49652022-06-017213113810.22052/mir.2022.243334.1322111967On the Riemann-Stieltjes IntegralAli Parsian0Department of Mathematics, Tafresh University, Tafresh, 39518-79611, I. R. IranThis study contributes to the theory of Riemann-Stieltjes integral. We prove that if all continuous piecewise linear functions are Riemann-Stieltjes integrable with respect to a bounded integrator α : [a,b] → R, then α must be of bounded variation on [a,b]. We also provide some other consequences.https://mir.kashanu.ac.ir/article_111967_38e1e40e7615202c24ada1b09fba3a91.pdfcantor’s intersection theoremfunction of bounded variationriemann-stieltjes integral |
| spellingShingle | Ali Parsian On the Riemann-Stieltjes Integral Mathematics Interdisciplinary Research cantor’s intersection theorem function of bounded variation riemann-stieltjes integral |
| title | On the Riemann-Stieltjes Integral |
| title_full | On the Riemann-Stieltjes Integral |
| title_fullStr | On the Riemann-Stieltjes Integral |
| title_full_unstemmed | On the Riemann-Stieltjes Integral |
| title_short | On the Riemann-Stieltjes Integral |
| title_sort | on the riemann stieltjes integral |
| topic | cantor’s intersection theorem function of bounded variation riemann-stieltjes integral |
| url | https://mir.kashanu.ac.ir/article_111967_38e1e40e7615202c24ada1b09fba3a91.pdf |
| work_keys_str_mv | AT aliparsian ontheriemannstieltjesintegral |