Informatic vs. Classical Differentiation on the Real Line

We study the relationship between informatic and classical difierentiation on the real line. The former arises when considering the interval domain over the reals equipped with the Lebesgue measurement. We show that informatic difierentiation is a strict generalization of its classical counterpart, and wonder if it can provide a springboard towards extending techniques and results from calculus to certain non classically difierentiable functions.