Let \(\lambda\) denote Lebesgue measure on \(\mathbb{R}^{n}\).

(i) Let \(u \in \mathcal{L}^{1}(\lambda)\) and \(K \subset \mathbb{R}^{n}\) be a compact (i.e. closed and bounded) set. Show that \(\lim _{|x| ightarrow \infty} \int_{K+x}|f| d \lambda=0\).

(ii) Let \(u\) be uniformly continuous and \(|f|^{p} \in \mathcal{L}^{1}(\lambda)\) for some \(p>0\). Show that \(\lim _{|x| ightarrow \infty} f(x)=0\).