0
$\begingroup$

Please, what is the difference between the following expressions "Lipschitz on any bounded set" and "Locally Lipschitz"?

$\endgroup$
3
$\begingroup$

The function $\sqrt x$ is locally Lipschitz on $(0,1)$ but is not Lipschitz on the bounded see $(0,1)$. This example is possible because $(0,1)$ is not compact.

As far as I can tell, the usual concept is Lipschitz on compact sets instead of on bounded sets. It is easy to prove that locally Lipschitz is equivalent to Lipschitz on compact sets.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.