Real Analysis Exchange

On continuous major and minor functions for the n-dimensional Perron integral

Benedetto Bongiorno, Luisa Di Piazza, and Valentin Skvortsov

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We prove that the \(n\)-dimensional Perron integral with respect to the full interval basis, without any regularity condition, defined by continuous major and minor functions is equivalent to the one defined by major and minor functions which are not supposed to be continuous.

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Real Anal. Exchange, Volume 22, Number 1 (1996), 318-327.

First available in Project Euclid: 1 June 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A39: Denjoy and Perron integrals, other special integrals 26A42: Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX] 26A45: Functions of bounded variation, generalizations

Perron integral basis of differentiation variation


Bongiorno, Benedetto; Di Piazza, Luisa; Skvortsov, Valentin. On continuous major and minor functions for the n -dimensional Perron integral. Real Anal. Exchange 22 (1996), no. 1, 318--327.

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