Quasi-norm (source code)

= Quasi-norm
{title2=$\|x+y\|\leq C(\|x\|+\|y\|)$}

A quasi-<norm> on a <vector space> is nonnegative, vanishes only at zero, is absolutely homogeneous, and satisfies a <triangle inequality> with one constant factor $C\geq1$. For $0<p<1$, $(\int|f|^p)^{1/p}$ on an <Lp space> is a quasi-<norm>: $\|f+g\|_p^p\leq\|f\|_p^p+\|g\|_p^p$ gives a quasi-<triangle inequality>. Measure-preserving composition preserves this quantity even though the <Minkowski inequality> is unavailable below exponent one.