Quasi-normed space

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 $L_p(E)$ with $0<p<1$, in which a quasi-norm is defined by the expression

$$ \| f \|_p = \left[ \int_E |f(x)|^p \; dx \right]^{1/p}, \quad f \in L_p(E) $$

#### Comments[edit]

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