Lebesgue's lemma

This article does not cite any sources. Please help by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources:  –  ·  ·  · scholar · JSTOR (December 2009) (Learn how and when to remove this template message)

For Lebesgue's lemma for open covers of compact spaces in topology see Lebesgue's number lemma

In mathematics, Lebesgue's lemma is an important statement in approximation theory. It provides a bound for the projection error.

Statement[]

Let (V, ||·||) be a normed vector space, U a subspace of V, and P a linear projector on U. Then for each v in V:

${\displaystyle \|v-Pv\|\leq (1+\|P\|)\inf _{u\in U}\|v-u\|.}$

See also[]

• Lebesgue constant (interpolation)