Lebesgue's lemma - Alchetron, The Free Social Encyclopedia

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 be a subspace of V and let P be a linear projector on U . Then, for each v in V:

∥ v − P v ∥ ≤ ( 1 + ∥ P ∥ ) inf u ∈ U ∥ v − u ∥ .

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