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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 1 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1338515223

Mathematical Reviews number (MathSciNet)
MR1433616

Zentralblatt MATH identifier
0879.26044

Subjects
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

Keywords
Perron integral basis of differentiation variation

Citation

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. https://projecteuclid.org/euclid.rae/1338515223


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References

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