Real Analysis Exchange

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

Eyad Massarwi and Paul Musial

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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

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

First available in Project Euclid: 4 April 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

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


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

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