Integral average ($⟨v{⟩}_E=|E{|}^{-1}{\int }_{E}v$)

The integral average of an integrable function over a measurable set $E$ of finite positive measure is $⟨v{⟩}_E=|E{|}^{-1}{\int }_{E}v$. Normalization removes the volume factor when comparing estimates on balls of different radii.