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