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The Riemann-Stieltjes integral: and some applications in complex analysis and probability theory
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2014 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

The purpose of this essay is to prove the existence of the Riemann-Stieltjes integral. After doing so, we present some applications in complex analysis, where we define the complex curve integral as a special case of the Riemann- Stieltjes integral, and then focus on Cauchy’s celebrated integral theorem. To show the versatility of the Riemann-Stieltjes integral, we also present some applications in probability theory, where the integral generates a general formula for the expectation, regardless of its underlying distribution. 

Place, publisher, year, edition, pages
2014. , 41 p.
National Category
Mathematical Analysis
URN: urn:nbn:se:umu:diva-89199OAI: diva2:719488
Educational program
Bachelor of Science in Physics and Applied Mathematics
Available from: 2014-06-18 Created: 2014-05-26 Last updated: 2015-06-09Bibliographically approved

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The Riemann-Stieltjes integral(857 kB)5610 downloads
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Leffler, Klara
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