Local conical dimensions for measures
  We study the decay of $\mu(B(x,r)\cap C)/\mu(B(x,r))$ as $r\downarrow 0$ for different kinds of measures $\mu$ on $\R^n$ and various cones $C$ around $x$. As an application, we provide sufficient conditions implying that the local dimensions can be calculated via cones almost everywhere. 
De-Jun Feng and Antti K\"aenm\"aki and Ville Suomala
math.CA