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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.

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Project Euclid (Hosted at Cornell University Library)  


Thomson, Brian S. - 

Id.: 55231022

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras claveRiemann sums - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2011 Michigan State University Press

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 0147-1937
[References] 1930-1219

Fecha de contribución: 08-may-2012


* Real Anal. Exchange 37, no. 1 (2011), 221-242

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