## Real Analysis Exchange

### A Vitali-like convergence theorem for the Henstock integral

Isidore Fleischer

#### 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

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

#### 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

#### References

• Russell A. Gordon, A general convergence theorem for non-absolute integrals, J. London Math. Soc., 2, no. 44 (1991), 301–309.
• Ke Cheng Liao, A Refinement of the controlled convergence theorem for Henstock integrals, Southeast Asian Bulletin of Mathematics, 11(1) (1987), 49–51.
• Peng-Yee Lee, Lanzhou Lectures on Henstock Integration, World Scientific, Singapore, 1989.
• Peng-Yee Lee and T. S. Chew, A better convergence theorem for Henstock integrals, Bull. London Math. Soc., 17 (1985), 557–564.
• Peng-Yee Lee and T. S. Chew, A short proof of the controlled convergence theorem for Henstock integrals, Bull. London Math. Soc., 19 (1987), 60–62.
• I. P. Natanson, Theory of functions of a real variable, Vol. 1, Ungar, New York, 1964.
• S. Saks, Theory of the integral, 2nd edition revised, Hafner Publications, New York, 1937.