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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
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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-Text
Keywords: p-integral; Riemann integral; Darboux integral p-integral; Riemann integral; Darboux integral
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Chen, R.-M. Equivalences of Riemann Integral Based on p-Norm. Mathematics 2018, 6, 168.

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