## Real Analysis Exchange

### On an Improvement of the Hake Theorem

Vasile Ene

#### Abstract

The well-known Hake Theorem asserts that if a function $f$ is Denjoy$^*$ integrable then it is also Perron integrable, and the two integrals are equal. In \cite{Ene1} we introduced a very strong Perron integration $({\mathcal P}_{1,1})$ and proved the corresponding Hake-type theorem, using the Vitali-Carath\'eodory Theorem. In this paper we give a new, less technical proof of this result, using essentially Lusin's Theorem.

#### Article information

Source
Real Anal. Exchange, Volume 24, Number 2 (1999), 867-873.

Dates
First available in Project Euclid: 28 September 2010

https://projecteuclid.org/euclid.rae/1285689162

Mathematical Reviews number (MathSciNet)
MR1704761

Zentralblatt MATH identifier
0967.26007

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

#### Citation

Ene, Vasile. On an Improvement of the Hake Theorem. Real Anal. Exchange 24 (1999), no. 2, 867--873. https://projecteuclid.org/euclid.rae/1285689162