Real Analysis Exchange

A Vitali-like convergence theorem for the Henstock integral

Isidore Fleischer

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Abstract

Theorem. If Henstock integrable \(f_n\) converge in measure to a finite \(f\) and their primitives \(F_n\) are equi-\(ACG_*\) and converge pointwise to a continuous \(F\) then \(\int f = \lim F_{n}\).

Article information

Source
Real Anal. Exchange, Volume 22, Number 1 (1996), 174-176.

Dates
First available in Project Euclid: 1 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1338515212

Mathematical Reviews number (MathSciNet)
MR1433605

Zentralblatt MATH identifier
0879.26033

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

Keywords
Vitali convergence Henstock integral

Citation

Fleischer, Isidore. A Vitali-like convergence theorem for the Henstock integral. Real Anal. Exchange 22 (1996), no. 1, 174--176. https://projecteuclid.org/euclid.rae/1338515212


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References

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