Warsaw: Polska Akademia Nauk * Instytut Matematyczny / Polish Academy of Sciences, Institute of Mathematics
Abstract:
A new approach to differentiation on a time scale T is presented. We give a suitable generalization of the Vitali Lemma and apply it to prove that every increasing function f:T→R has a right derivative f′+(x) for μΔ-almost all x∈T. Moreover, ∫[a,b)f′+(x)dμΔ≤f(b)−f(a).
