Recent content by peb78

  1. P

    Graduate Value of a measure theoretic integral over a domain shrinking to a single set

    That's exactly what I'm looking for. Thanks!
  2. P

    Graduate Value of a measure theoretic integral over a domain shrinking to a single set

    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...