Lebesgue's lemma


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.

tatement

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_{uin U}|v-u|.

ee also

* Lebesgue constant (interpolation)


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