= Density point
{title2=$\lim_{r\downarrow0}|A\cap B(x,r)|/|B(x,r)|=1$}
= Lebesgue density point
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{synonym}
A point at which a measurable set occupies an asymptotically full fraction of small balls, as expressed above with <Lebesgue measure>. The <Lebesgue density theorem> says that almost every point of a measurable set is a density point. On the real line, the same limiting conclusion holds for arbitrary shrinking intervals containing that point, since each interval lies in a centered interval of at most twice its length.
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