On Covering Systems
Donald J. Mallory, Maurice Sion · Canadian Journal of Mathematics · 1964
Differentiation of a set function μ with respect to another v at a point x involves taking the limit of the ratio μA/vA as A "converges" to x in some sense which requires that A belong to some family of sets N(x) (e.g. spheres with centre x). For the development of a reasonable theory of differentiation certain restrictions must be placed on the families N(x). The best-known restriction is that they form a Vitali system. However, other systems have been considered.