Currently I'm working through a proof in which occours the following limsup:
$\limsup_{||h||\to 0} |f(h)|$
In the internet I only found definitions for the following limits: $\lim_{n \to \infty}$ and $\lim_{x \to \xi}$. Where can I find the proper definition?
Suppose $f : \mathbb{R}^n \to \mathbb{R}$. Then $$ \limsup_{\|h\| \to 0} | f(h) | = \lim_{\varepsilon \to 0} \ \sup_{\| h \| \leq \varepsilon} |f(h)| $$ where $\varepsilon > 0$.