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2002-2003 The sharp Riesz-type definition for the Henstock-Kurzweil integral.
Tuo-Yeong Lee
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Real Anal. Exchange 28(1): 55-71 (2002-2003).


In this paper, we prove that if $f$ is Henstock-Kurzweil integrable on a compact subinterval $[a,b]$ of the real line, then the following conditions are satisfied: (i) there exists an increasing sequence $\{X_n\}$ of closed sets whose union is $[a,b]$; (ii) $\{f{\chi_{ _{X_n}}}\}$ is a sequence of Lebesgue integrable functions on $[a,b]$; (iii) the sequence $\{f{\chi_{ _{X_n}}}\}$ is Henstock-Kurzweil equi-integrable on $[a,b]$. Subsequently, we deduce that the gauge function in the definition of the Henstock-Kurzweil integral can be chosen to be measurable, and an indefinite Henstock-Kurzweil integral generates a sequence of uniformly absolutely continuous finite variational measures.


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Tuo-Yeong Lee. "The sharp Riesz-type definition for the Henstock-Kurzweil integral.." Real Anal. Exchange 28 (1) 55 - 71, 2002-2003.


Published: 2002-2003
First available in Project Euclid: 12 June 2006

zbMATH: 1044.26007
MathSciNet: MR1973968

Primary: 26A39

Keywords: equi-integrability , Henstock-Kurzweil integral

Rights: Copyright © 2002 Michigan State University Press

Vol.28 • No. 1 • 2002-2003
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