Let \((S, d)\) be a complete metric space equipped with the \(\sigma\)-algebra \(\mathscr{B}(S)\) of its Borel sets. Assume that \(\left(X_{n}ight)_{n \geqslant 1}\) is a sequence of \(S\)-valued random variables such that

\[\lim _{n ightarrow \infty} \sup _{m \geqslant n} \mathbb{E}\left(d\left(X_{n}, X_{m}ight)^{p}ight)=0\]

for some \(p \in[1, \infty)\). Show that there is a subsequence \(\left(n_{k}ight)_{k \geqslant 1}\) and a random variable \(X\) such that \(\lim _{k ightarrow \infty} X_{n_{k}}=X\) almost surely.