In this paper, as picture below, what is the mean of proof of Lemma 2.3? I absolutly can't understand it. And how to get almost any $\epsilon > 0$ is regular from Sard theorem ? Sard theorem just say critical set has measure 0.
I want a way , if $Z_\phi$ is density in $S$ , then , $\forall x\in Z_\phi$ , I can find $\{x_n\}\subset Z_\phi$ and $x_n\rightarrow x$ , then $$ \nabla\phi(x)=\lim\limits_{n\rightarrow\infty} \frac{\phi(x_n)-\phi(x)}{x_n-x}=0 $$ But , how to show $Z_\phi$ is density in $S$ ?
