Simple Vitali Lemma

Let E be a subset of \mathbb{R}^n with |E|_e<\infty, and let K be a collection of cubes Q covering E. Then there exist a positive constant \beta (depending only on n), and a finite number of disjoint cubes Q_1,\dots,Q_N in K such that \displaystyle \sum_{j=1}^N|Q_j|\geq\beta|E|_e.
(We may take 0<\beta<5^{-n}.)

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