- #1

Vulture1991

- 7

- 0

\lim_{\epsilon\rightarrow 0}~\max_{x\in \mathcal{Z}_\epsilon}~\text{dist}(x, \mathcal{Z})=0,

[/TEX]holds?

I know in general this doesn't hold by this example (function of a scalar variable):

[TEX]

f(x)=\left\{\begin{align}

0,\quad{x\leq 0};

\\

1/x,\quad x>0.

\end{align}

\right.

[/TEX]

I really appreciate any help or hint.

Thank you.