Volume average
= Volume average
{title2=$\langle f\rangle_V=V^{-1}\int_V f\,d^3x$}
A <volume average> is the normalized <integral average> of a field over a three-dimensional region of finite positive <volume>. For a fixed region, differentiating in time commutes with this average under the usual regularity conditions. The <divergence theorem> converts the average of a divergence into its net boundary flux divided by volume.