Lebesgue's lemma

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:

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See also

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