Real Analysis Exchange

A Stieltjes Type Extension of the $L^{r}$-Perron Integral

Eyad Massarwi and Paul Musial

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Abstract

We explore properties of $L^{r}$-derivates with respect to a monotone increasing Lipschitz function. We then define $L^{r}$-ex-major and $L^{r}$-ex-minor functions with respect to a monotone increasing Lipschitz function and use these to define a Perron-Stieltjes-type integral which extends the integral of L. Gordon.

Article information

Source
Real Anal. Exchange, Volume 40, Number 2 (2015), 291-308.

Dates
First available in Project Euclid: 4 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.rae/1491271218

Mathematical Reviews number (MathSciNet)
MR3499766

Zentralblatt MATH identifier
1384.26031

Subjects
Primary: 26A42: Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX] 26A39: Denjoy and Perron integrals, other special integrals
Secondary: 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15]

Keywords
$L^r$-derivative Lipschitz Perron Integral Perron-Stieltjes Integral

Citation

Massarwi, Eyad; Musial, Paul. A Stieltjes Type Extension of the $L^{r}$-Perron Integral. Real Anal. Exchange 40 (2015), no. 2, 291--308. https://projecteuclid.org/euclid.rae/1491271218


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