Real Analysis Exchange

Convergence theorems for the Henstock integral involving small Riemann sums.

Soeparna Darmawijaya, Ch. Rini Indrati, Bambang Soedijono, and Subanar

Full-text: Open access

Abstract

We generalize the functionally-small-Riemann-sum (FSRS) property for the Henstock integral to the $n$-dimensional Euclidean space. We prove a convergence theorem and its connection with the equi-integrability condition.

Article information

Source
Real Anal. Exchange, Volume 29, Number 1 (2003), 481-488.

Dates
First available in Project Euclid: 9 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.rae/1149860209

Mathematical Reviews number (MathSciNet)
MR2063089

Zentralblatt MATH identifier
1071.26006

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

Keywords
Henstock Integral $\delta$-fine partition Functionally Small Riemann Sum Uniformly Functionally Small Riemann sum Uniformly Strong Lusin Condition Equi-Henstock integrability

Citation

Indrati, Ch. Rini; Darmawijaya, Soeparna; Soedijono, Bambang; Subanar. Convergence theorems for the Henstock integral involving small Riemann sums. Real Anal. Exchange 29 (2003), no. 1, 481--488. https://projecteuclid.org/euclid.rae/1149860209


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