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.
