A Probabilistic Proof of the Vitali Covering Lemma

Date
2017-04-25
Authors
Gwaltney, Ethan
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Abstract

The Vitali Covering Lemma states that, given a finite collection of balls in R^d, there exists a disjoint subcollection that fills at least 3^{−d} of the measure of the union of the original collection. We present classical proofs of this lemma due to Banach and Garnett. Subsequently, we provide a new proof of this lemma that utilizes probabilistic “Erdo ̈s” type techniques and Padovan numbers.

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Mathematics
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