Lebesgue point
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 . References

Mathematical analysis