Hi. Under what conditions does the following equality hold?
f(x)=\lim\limits_{\Omega\rightarrow\{x\}} \frac{1}{\mu(\Omega)}\int_\Omega f d\mu
where \mu is some measure. Being a little more careful, let \Omega_i be a sequence of sets such that \Omega_{i+1}\subseteq\Omega_i and...