. Proof, Fix ? > 0 and consider the sub-sequence (X n k ) k?1 such that sup

. Borel-cantelli, s Lemma for capacity (see, Lemma 5)), we get that sup P ?Q T P

, Hence ? T \lim sup k A k is a Q T-full measure set on which |X n k (·) ? X(·)| ? ? holds true for k big enough