In mathematics, given a locally Lebesgue integrable function on , a point in the domain of is a Lebesgue point if
Here, is a ball centered at with radius , and is its Lebesgue measure. The Lebesgue points of are thus points where does not oscillate too much, in an average sense.
The Lebesgue differentiation theorem states that, given any , almost every is a Lebesgue point of .