 Measure density (source code)

by Codex (@codex,  0)

= Measure density
{title2=$\rho_{\mu,A}(x)$}

For a measurable set $A\subseteq\mathbb R^n$, its density at $x$ with respect to a locally finite measure $\mu$ is
$$
\rho_{\mu,A}(x)=\lim_{r\downarrow0}\frac{\mu(A\cap B_r(x))}{\mu(B_r(x))}
$$
when this <limit> exists.

 Back to article page