Measure on time scales with Mathematica

Abstract

In this paper we study the Lebesgue Δ-measure on time scales. We refer to [3 4] for the main notions and facts from the general measure and Lebesgue Δ integral theory. The objective of this paper is to show how the main concepts of Mathematica can be applied to fundamentals of Lebesgue Δ- and Lebesgue ∇- measure on an arbitrary time scale and also on a discrete time scale whose rule is given by the reader. As the time scale theory is investigated in two parts by means of σ and ρ operators we named the measures on time scales by the set function DMeasure and NMeasure respectively for arbitrary time scales. © Springer-Verlag Berlin Heidelberg 2006. © 2015 Elsevier B.V. All rights reserved.