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1998/1999 On an Improvement of the Hake Theorem
Vasile Ene
Real Anal. Exchange 24(2): 867-873 (1998/1999).


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.


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Vasile Ene. "On an Improvement of the Hake Theorem." Real Anal. Exchange 24 (2) 867 - 873, 1998/1999.


Published: 1998/1999
First available in Project Euclid: 28 September 2010

zbMATH: 0967.26007
MathSciNet: MR1704761

Primary: 26A39

Keywords: $AC^*G$ , the Kurzweil-Henstock integral , the Perron integral

Rights: Copyright © 1999 Michigan State University Press

Vol.24 • No. 2 • 1998/1999
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