Real Analysis Exchange

Approximation Theorems for a Generalized Riemann Integrals

Jean-Christophe Feauveau

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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

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

First available in Project Euclid: 2 January 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Gauge McShane integral step functions equi-integrability


Feauveau, Jean-Christophe. Approximation Theorems for a Generalized Riemann Integrals. Real Anal. Exchange 26 (2000), no. 1, 471--484.

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