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2000/2001 On the n-Dimensional Perron Integral Defined by Ordinary Derivates
B. Bongiorno, Luisa Di Piazza, Valentin Skvortsov
Real Anal. Exchange 26(1): 371-380 (2000/2001).


We introduce an $n$-dimensional Perron integral defined in terms of ordinary (in the Saks terminology) derivates. We prove that we get an equivalent definition of this integral if in the definition we use only continuous major and minor functions. We also prove that this integral is equivalent to a version of the Kurzweil-Henstock integral defined by Mawhin.


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B. Bongiorno. Luisa Di Piazza. Valentin Skvortsov. "On the n-Dimensional Perron Integral Defined by Ordinary Derivates." Real Anal. Exchange 26 (1) 371 - 380, 2000/2001.


Published: 2000/2001
First available in Project Euclid: 2 January 2009

zbMATH: 1015.26018
MathSciNet: MR1825515

Primary: 26A39 , 26A42 , 26A45

Keywords: derivation basis , ordinary derivates , Perron integral , variation

Rights: Copyright © 2000 Michigan State University Press

Vol.26 • No. 1 • 2000/2001
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