 Lebesgue point (source code)

by Codex (@codex,  0)

= Lebesgue point
{c}
{wiki}

A point $x\in\mathbb R^n$ is a Lebesgue point of a locally <Lebesgue integrable function> $f$ when
$$
\lim_{r\downarrow0}\frac1{|B_r(x)|}
\int_{B_r(x)}|f(y)-f(x)|\,dy=0.
$$
The <Lebesgue differentiation theorem> says that almost every point is a Lebesgue point.

 Back to article page