Quasi-normed space

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A linear space on which a quasi-norm is given. An example of a quasi-normed space that is not normed is the Lebesgue space with , in which a quasi-norm is defined by the expression


The quasi-normed topological vector spaces are precisely the locally bounded topological vector spaces, cf. Quasi-norm.

How to Cite This Entry:
Quasi-normed space. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article