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 $\nabla$- 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.