Mathematics 2018, 6(9), 168; https://doi.org/10.3390/math6090168
Equivalences of Riemann Integral Based on p-Norm
School of Mathematics and Statistics, Baise University, No.21 Zhongshan Road, Baise 533000, Guangxi, China
Received: 11 August 2018 / Revised: 6 September 2018 / Accepted: 6 September 2018 / Published: 13 September 2018
Abstract
In the usual Riemann integral setting, the Riemann norm or a mesh is adopted for Riemann sums. In this article, we use the p-norm to define the p-integral and show the equivalences between the Riemann integral and the p-integral. The p-norm provides an alternative approach to define the Riemann integral. Based on this norm, we also derive some other equivalences of the Riemann integral and the p-integral. View Full-TextKeywords:
p-integral; Riemann integral; Darboux integral
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Chen, R.-M. Equivalences of Riemann Integral Based on p-Norm. Mathematics 2018, 6, 168.
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