In mathematics, Lebesgue's lemma is an important statement in approximation theory. It provides a bound for the projection error. Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations by or about: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... In mathematics, approximation theory is concerned with how functions can be approximated with other, simpler, functions, and with characterising in a quantitative way the errors introduced thereby. ...
Statement
Let (V, ||·||) be a normed vector space, (Ui)i∈N be a family of subspaces of V and for each i let Pi be a linear projector on Ui. Then, for each v in V and each i in N: In mathematics, with 2- or 3-dimensional vectors with real-valued entries, the idea of the length of a vector is intuitive and can be easily extended to any real vector space Rn. ... In mathematics, an index set is another name for a function domain. ... In linear algebra, a projection is a linear transformation P such that P2 = P, i. ...
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