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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.31 No.4

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Riemann-Stieltjes Integrals and their Representing Measures

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2024, v.31 no.4, pp.453-476
https://doi.org/10.7468/jksmeb.2024.31.4.453
Lee Joong Kwoen (Dongguk University)
Han Ju Lee (Dongguk University)
Lee, J. K. , & Han, J. L. (2024). Riemann-Stieltjes Integrals and their Representing Measures, 31(4), 453-476, https://doi.org/10.7468/jksmeb.2024.31.4.453

Abstract

The Riemann-Stieltjes integrals of continuous functions with respect to a function of bounded variation can be represented by a regular, Borel, complex measure. In this paper, we study the link between the Riemann-Stieltjes integral and measure theory using this representation. Specifically, we investigate the Riemann-Stieltjes integrability and its measurability. Furthermore, we derive a criterion for Riemann-Stieltjes integrability through a method di erent from known proofs. In particular, we calculate the upper and lower Riemann-Stieltjes integrals with respect to a monotone increasing function.

keywords
Riemann-Stieltjes integral, Lebesgue-Stiletjes integral, Riesz representation

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics

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