Complex sentence: By the Vitali lemma, we may choose a disjoint subcollection\\ of this collection which is disjoint and, by tripling their radii, will contain the area covered by the original collection of balls, and hence will cover E.
Split into simpler sentences: By the Vitali lemma, we may choose a subcollection\\ which is disjoint. Then, by tripling their radii, this transformed subcollection will contain the area covered by the original collection of balls, and hence will cover E.