- 期刊
A NOTE ON RIEMANN INTEGRABILITY
並列摘要
In this note we define Riemann integrability for real valued functions defined on a compact metric space accompanied by a finite Borel measure. If the measure of each open ball equals the measure of its corresponding closed ball, then a bounded function is Riemann integrable if and only if its set of points of discontinuity has measure zero.
延伸閱讀
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- BLAYA, R. A., REYES, J. B., & PEÑA, D. P. (2005). RIEMANN BOUNDARY VALUE PROBLEM FOR HYPERANALYTIC FUNCTIONS. International Journal of Mathematics and Mathematical Sciences, 2005(), 2821-2840-229. https://doi.org/10.1155/IJMMS.2005.2821
- Roy, R. (1984). THE SERRE DUALITY THEOREM FOR RIEMANN SURFACES. International Journal of Mathematics and Mathematical Sciences, 1984(), 397-402. https://doi.org/10.1155/S0161171284000405
- Huang, H. W. (2018). A Proof of Riemann-Roch Theorem by Algebraic Methods [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU201801660
- Liu, G. (2022). Comparative Study of Riemann and Lebesgue Integrals. International Core Journal of Engineering, 8(9), 94-100. https://doi.org/10.6919/ICJE.202209_8(9).0015