Definition talk:Lipschitz Norm

Is this the only norm that is possible to be formed on this space?

If so, then write a uniqueness proof.

If not, then this norm needs to be given a unique name, and you can't refer to it as "the norm". --prime mover (talk) 07:37, 28 December 2022 (UTC)


 * Not unique, $\size\cdot_\infty$ is another important norm. We need a name for $\norm \cdot_\theta$. --Usagiop (talk) 11:59, 28 December 2022 (UTC)


 * If it hasn't got one, we can call it the Lipschitz norm and invoke the neologism template in a linguistic note. I can't find the concept of "Lipschitz norm" by a cursory googling, so we may be golden.


 * We will probably find the $\infty$ version is the same as the supremum norm, so we can probably call it that.


 * Yes, Lipschitz norm is surely correct. Or, Hölder $C^{0,1}$ norm, as this is the $\norm \cdot_{\map {C^{0,1} }{F_\theta} }$ of Hölder space. --Usagiop (talk) 13:43, 28 December 2022 (UTC)