How to prove the following:
$\lambda$ is a measure on $R^d$ which is singular w.r.t lebesgue measure $m$. Then $\text{lim sup}_{r\rightarrow 0}\frac{\lambda (B(r,x))}{m (B(r,x))} =0$ $m$-almost everywhere.
Note: $B(r,x)$ is a ball centered at $x$ with radius $r$.
Could anyone provide me with the first step or a hint?
Does it relate to the shrinking rate?