Lebesgue point

In mathematics, given a locally Lebesgue integrable function

is a Lebesgue point if[1] Here,

is a ball centered at

with radius

is its Lebesgue measure.

The Lebesgue points of

does not oscillate too much, in an average sense.

[2] The Lebesgue differentiation theorem states that, given any

is a Lebesgue point of