Turkish Journal of Mathematics
DOI
10.3906/mat-0711-11
Abstract
The theory of time scales was introduced by Stefan Hilger in his Ph. D. thesis in 1988, supervised by Bernd Auldbach, in order to unify continuous and discrete analysis [5]. Measure theory on time scales was first constructed by Guseinov [4], then further studies were made by Guseinov-Bohner [1], Cabada-Vivero [2] and Rzezuchowski [6]. In this article, we adapt the concept of Lebesgue-Stieltjes measure to time scales. We define Lebesgue-Stieltjes \Delta and \nabla-measures and by using these measures, we define an integral adapted to time scales, specifically Lebesgue-Stieltjes \Delta-integral. We also establish the relation between Lebesgue-Stieltjes measure and Lebesgue-Stieltjes \Delta-measure, consequently between Lebesgue-Stieltjes integral and Lebesgue-Stieltjes \Delta- integral.
Keywords
Time scales, Lebesgue-Stieltjes \Delta-measure, Lebesgue-Stieltjes \Delta-integral.
First Page
27
Last Page
40
Recommended Citation
DENİZ, ASLI and UFUKTEPE, ÜNAL
(2009)
"Lebesgue-Stieltjes Measure on Time Scales,"
Turkish Journal of Mathematics: Vol. 33:
No.
1, Article 4.
https://doi.org/10.3906/mat-0711-11
Available at:
https://journals.tubitak.gov.tr/math/vol33/iss1/4
