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:

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

See also

Lebesgue constant (interpolation)

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.