## Real Analysis Exchange

### Some comments on the H1-integral.

Piotr Sworowski

#### Abstract

In this note we consider two natural attempts to give a descriptive characterization for $H_1$-primitives, and discuss why these attempts fail. Meanwhile we get a new descriptive definition of the Henstock integral. Also, we prove that every Henstock integrable function can be written as a sum of a Lebesgue integrable and an $H_1$-integrable ones.

#### Article information

Source
Real Anal. Exchange, Volume 29, Number 2 (2003), 789-798.

Dates
First available in Project Euclid: 7 June 2006

https://projecteuclid.org/euclid.rae/1149698540

Mathematical Reviews number (MathSciNet)
MR2083813

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

#### Citation

Sworowski, Piotr. Some comments on the H 1 -integral. Real Anal. Exchange 29 (2003), no. 2, 789--798. https://projecteuclid.org/euclid.rae/1149698540

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