A computational aspect of the Lebesgue differentiation theorem
Pathak · Journal of Logic and Analysis · 2009
Given an L 1 -computable function, f , we identify a canonical representative of the equivalence class of f , where f and g are equivalent if and only if |f -g| is zero.Using this representative, we prove a modified version of the Lebesgue Differentiation Theorem.Our theorem is stated in terms of Martin-Löf random points in Euclidean space.