Real Analysis Exchange

Approximation Theorems for a Generalized Riemann Integrals

Jean-Christophe Feauveau

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Abstract

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.

Article information

Source
Real Anal. Exchange, Volume 26, Number 1 (2000), 471-484.

Dates
First available in Project Euclid: 2 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.rae/1230939179

Mathematical Reviews number (MathSciNet)
MR1825529

Zentralblatt MATH identifier
1022.28004

Subjects
Primary: 26A39: Denjoy and Perron integrals, other special integrals 28B05: Vector-valued set functions, measures and integrals [See also 46G10]

Keywords
Gauge McShane integral step functions equi-integrability

Citation

Feauveau, Jean-Christophe. Approximation Theorems for a Generalized Riemann Integrals. Real Anal. Exchange 26 (2000), no. 1, 471--484. https://projecteuclid.org/euclid.rae/1230939179


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References

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