The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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RIEMANN-STIELTJES INTEGRALS AND THEIR REPRESENTING MEASURES

  • Joong Kwoen Lee (Department of Mathematics Education, Dongguk University) ;
  • Han Ju Lee (Department of Mathematics Education, Dongguk University)
  • Received : 2024.08.07
  • Accepted : 2024.10.05
  • Published : 2024.11.30
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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 different from known proofs. In particular, we calculate the upper and lower Riemann-Stieltjes integrals with respect to a monotone increasing function.

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Acknowledgement

The second named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology [NRF-2020R1A2C1A01010377].

References

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