It's about the following exercise:
$i)$ Let $h: \mathbb{R} \rightarrow \mathbb{R}$ with $h(x)=\begin{cases} a,\; 0 \leq x < \lambda \\ b, \; \lambda \leq x < 1.\end{cases}$. The function $h$ can be continued periodically on $\mathbb{R}$ and let $w_n(x)=h(nx)$. Determine the Young measure generated by $\{w_n\}$.
$ii)$ Let $h:[0,1]^n \rightarrow \mathbb{R}$ be integrable. Continue $h$ periodically on $\mathbb{R}^n$ and let $w_n(x)=h(nx)$. Determine the Young measure generated by $\{w_n\}$.
I was able to do the first exercise. The Young measure is $\nu(x)=\lambda\delta_{\{a\}}+(1-\lambda)\delta_{\{b\}}$. But I am not really sure that I understand $ii)$ correctly: I suppose the $h$ in $ii)$ is the same $h$ as in $i)$, only with arguments in $\mathbb{R}^n$? But if this is true, shouldn't the Young measure be the same as in $i)$? And if not, why not and why can't I prove this the same way I proved $i)$? I would appreciate a little help with exercise $ii)$ because it isn't completely clear to me where exactly the difference to exercise $i)$ is.