Lebesgue point

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Lebesgue point by

Codex  0 2026-09-24

A point

x \in R^{n}

is a Lebesgue point of a locally Lebesgue integrable function

f

when

lim_{r ↓ 0} \frac{1}{∣ B _{r} ( x ) ∣} \int_{B_{r} (x)} ∣ f (y) - f (x) ∣ d y = 0.

The Lebesgue differentiation theorem says that almost every point is a Lebesgue point.

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