Regularities of general Hausdorff and packing functions.

• One of the most important single results for the Lebesgue measure is the Lebesgue density theorem. • Marstrand's Theorem asserts that density in the Euclidean space can exist only if the dimension is an integer. • Tricot established related results in a more general context. • In this work, we prove a decomposition theorem of Besicovitch's type for the regularities of general Hausdorff and packing functions. • We try to formulate another version of Tricot's density theorem. We prove a decomposition theorem of Besicovitch's type for the regularities of general Hausdorff and packing functions. As an application, we try to formulate another version of Tricot's density theorem. [ABSTRACT FROM AUTHOR]