Turkish Journal of Mathematics
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.
DOI
10.3906/mat-0711-11
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