Real Analysis Exchange

The fundamental theorem of calculus for \(\text{GR}_k\)-type integrals.

D. K. Ganguly, Supriya Pal, and Lee Peng Yee

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Abstract

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.

Article information

Source
Real Anal. Exchange, Volume 28, Number 2 (2002), 549-563.

Dates
First available in Project Euclid: 20 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.rae/1184963816

Mathematical Reviews number (MathSciNet)
MR2010336

Subjects
Primary: 26A39: Denjoy and Perron integrals, other special integrals

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

Citation

Pal, Supriya; Ganguly, D. K.; Yee, Lee Peng. The fundamental theorem of calculus for \(\text{GR}_k\)-type integrals. Real Anal. Exchange 28 (2002), no. 2, 549--563. https://projecteuclid.org/euclid.rae/1184963816


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