The authors studies relations between rectifiability properties of Borel measures in and some singular integrals with respect to them. Let be the norm in and the closed ball with center and radius , and let be a Borel regular measure. Let
The m-dimensional lower density of the measure at the point is defined by
A measure is said to be rectifiable if there exist dimensional submanifolds such that , and should be absolutely continuous with respect to the dimensional Hausdorff measure . One of the main result states that, if is a finite Borel measure in and if and exist for almost all , then is rectifiable.