A computational aspect of the Lebesgue differentiation theorem

Given an L1 -computable function, f , we identify a canonical represen- tative of the equivalence class of f , where f and g are equivalent if and only if R jf gj is zero. Using this representative, we prove a modified version of the Lebesgue Differentiation Theorem. Our theorem is stated in terms of Martin-L¨ random points in Euclidean space. 2000 Mathematics Subject Classification 03D80 (primary); 26A24 (secondary)