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2000/2001 Approximation Theorems for a Generalized Riemann Integrals
Jean-Christophe Feauveau
Real Anal. Exchange 26(1): 471-484 (2000/2001).


This note concerns the generalized Riemann integrals using free tagged subdivisions, and leading to absolute integration theories. We first establish an approximation theorem by step functions. This result will allow us to define a natural notion of equi-integrability in Lebesgue space $L^1$. Some applications, as a new caracterization of compact parts of $L^1$, are presented.


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Jean-Christophe Feauveau. "Approximation Theorems for a Generalized Riemann Integrals." Real Anal. Exchange 26 (1) 471 - 484, 2000/2001.


Published: 2000/2001
First available in Project Euclid: 2 January 2009

zbMATH: 1022.28004
MathSciNet: MR1825529

Primary: 26A39 , 28B05

Keywords: equi-integrability , gauge , McShane integral , step functions

Rights: Copyright © 2000 Michigan State University Press

Vol.26 • No. 1 • 2000/2001
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