E. Gwaltney

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Articles: 1

A probabilistic proof of the Vitali Covering Lemma

E. Gwaltney, P. Hagelstein, D. Herden

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 24 (2018), no. 1, 34-40

The classical Vitali Covering Lemma on $\mathbb{R}$ states that there exists a constant $c > 0$ such that, given a finite collection of intervals $\{I_j\}$ in $\mathbb{R}$, there exists a disjoint subcollection $\{\tilde{I}_j\} \subseteq \{I_j\}$ such that $|\cup \tilde{I}_j| \geq c |\cup I_j|$. We provide a new proof of this covering lemma using probabilistic techniques and Padovan numbers.

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