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2002/2003 The fundamental theorem of calculus for \(\text{GR}_k\)-type integrals.
D. K. Ganguly, Supriya Pal, Lee Peng Yee
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Real Anal. Exchange 28(2): 549-563 (2002/2003).


The \(GR_k\) integral, a Stieltjes type integral, was introduced by the authors. In this paper we introduce a \(GR_k\)-type integral that admits the fundamental theorem of calculus. Also, a convergence theorem is proved using equi-integrability conditions.


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D. K. Ganguly. Supriya Pal. Lee Peng Yee. "The fundamental theorem of calculus for \(\text{GR}_k\)-type integrals.." Real Anal. Exchange 28 (2) 549 - 563, 2002/2003.


Published: 2002/2003
First available in Project Euclid: 20 July 2007

MathSciNet: MR2010336

Primary: 26A39

Keywords: $\delta^{k}$-fine division , $BV^{k}$ , $g$ regular function , $g^{k}$-variation , $GR_k$-integral , $GR_k^*$-integral , $LBV^k$ , Equiintegrability , Henstock integral , nearly additive function. , regulated $\delta^k$-fine division , Saks-Henstock Lemma

Rights: Copyright © 2002 Michigan State University Press

Vol.28 • No. 2 • 2002/2003
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