Annales Academić Scientiarum Fennicć
Mathematica
Volumen 36, 2011, 153-164

AN ELEMENTARY WAY TO INTRODUCE A PERRON-LIKE INTEGRAL

Hana Bendová and Jan Malý

Charles University, Department of Mathematical Analysis
Sokolovská 83, 186 00 Prague 8, Czech Republic; haaanja 'at' gmail.com

Charles University, Department of Mathematical Analysis
Sokolovská 83, 186 00 Prague 8, Czech Republic, and
J.E. Purkyne University, Department of Mathematics
Ceské mládeze 8, 400 96 Ústí nad Labem, Czech Republic; maly 'at' karlin.mff.cuni.cz

Abstract. We give an alternative definition of integral at the generality of the Perron integral and propose an exposition of the foundations of integral theory starting from this new definition. Both definition and proofs needed for the development are unexpectedly simple. We show how to adapt the definition to cover the multidimensional and Stieltjes case and prove that our integral is equivalent to the Henstock-Kurzweil(-Stieltjes) integral.

2000 Mathematics Subject Classification: Primary 26A39; Secondary 26A24, 26A36.

Key words: Perron integral, Henstock-Kurzweil integral.

Reference to this article: H. Bendová and J. Malý: An elementary way to introduce a Perron-like integral. Ann. Acad. Sci. Fenn. Math. 36 (2011), 153-164.

Full document as PDF file

doi:10.5186/aasfm.2011.3609