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Lebesgue's lemma - Wikipedia, the free encyclopedia

Lebesgue's lemma

From Wikipedia, the free encyclopedia

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

[edit] Statement

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

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

[edit] See also

Lebesgue constant (interpolation)

Retrieved from "http://en.wikipedia.org../../../l/e/b/Lebesgue%27s_lemma.html"

Categories: Lemmas | Approximation theory

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