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 . Measure theory on time scales was first constructed by Guseinov , then further studies were made by Guseinov-Bohner , Cabada-Vivero  and Rzezuchowski . 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.
Time scales, Lebesgue-Stieltjes \Delta-measure, Lebesgue-Stieltjes \Delta-integral.
DENİZ, ASLI and UFUKTEPE, ÜNAL
"Lebesgue-Stieltjes Measure on Time Scales,"
Turkish Journal of Mathematics: Vol. 33:
1, Article 4.
Available at: https://journals.tubitak.gov.tr/math/vol33/iss1/4