Is $L^p$ for $0<p<1$ quasi-normed?
It follows from the inequality $(a+b)^p\leq a^p+b^p$ and the convexity of $x\mapsto x^{1/p}$ for $0<p<1$.
Is $L^p$ for $0<p<1$ quasi-normed?
It follows from the inequality $(a+b)^p\leq a^p+b^p$ and the convexity of $x\mapsto x^{1/p}$ for $0<p<1$.