Translator Disclaimer
2011/2012 On Riemann Sums
Brian S. Thomson
Real Anal. Exchange 37(1): 221-242 (2011/2012).

Abstract

If a sum of the form \[\sum_{i=1}^n f(\xi_i)(x_i-x_{i-1})\] is used without the familiar requirement that the sequence of points \(a=x_0, x_1, \dots, x_n=b\) is increasing, do we still get a useful approximation to the integral? With a suitable set of hypotheses the answer is yes. We give applications to change of variable formulas and the problem of characterizing derivatives.

Citation

Download Citation

Brian S. Thomson. "On Riemann Sums." Real Anal. Exchange 37 (1) 221 - 242, 2011/2012.

Information

Published: 2011/2012
First available in Project Euclid: 30 April 2012

MathSciNet: MR3016862

Subjects:
Primary: 26A24, 26A42

Rights: Copyright © 2011 Michigan State University Press

JOURNAL ARTICLE
22 PAGES


SHARE
Vol.37 • No. 1 • 2011/2012
Back to Top