Definition 24.7.2 (Average).label Let $\mu: \cb_{\real^d}\to [0, \infty]$ be a regular Borel measure on $\real^{d}$ and $m$ be the Lebesgue measure on $\real^{d}$, then
\[(0, \infty) \times \real^{d} \to [0, \infty) \quad (r, x) \mapsto A_{r}\mu(x) = \frac{\mu(B_{\real^d}(x, r))}{m(B_{\real^d}(x, r))}\]
is the average of $\mu$ on $B_{\real^d}(x, r)$.
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