Spherical derivative of a measure
= Spherical derivative of a measure
{title2=$D_s\mu(x)=\lim_{r\downarrow0}\mu(B(x,r))/\lambda_d(B(x,r))$}
The spherical <derivative> compares the mass of shrinking centered <open balls> with their <Lebesgue measure>, when the limit exists. This is a density of one <measure> relative to Euclidean volume, rather than the relative density of a set within one fixed <measure>. A singular finite <Borel measure> has spherical <derivative> zero <Lebesgue almost everywhere>.