Just to be clear, a quasi-norm is like a norm but instead of genuine subadditivity we have(adsbygoogle = window.adsbygoogle || []).push({});

##||x+y||\leq C(||x||+||y||)## where ##C\geq1## is some fixed constant.

To be honest, other than trivial examples the only one that comes to mind is ##L^p## for ##p\in(0,1)##. A quick google search doesn't yield much.

More generally, how about quasi-metric spaces? Similarly the triangle inequality is weakened to have a fixed multiplicative constant out front.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Can you think of quasi-norms which aren't norms?

**Physics Forums | Science Articles, Homework Help, Discussion**