Open Access

A probabilistic proof of the Vitali Covering Lemma

Abstract

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.

Key words: Differentiation of integrals, covering lemmas, probabilistic method.

Article Information

 Title A probabilistic proof of the Vitali Covering Lemma Source Methods Funct. Anal. Topology, Vol. 24 (2018), no. 1, 34-40 MathSciNet MR3783816 Milestones Received 13/08/2017; Revised 06/09/2017 Copyright The Author(s) 2018 (CC BY-SA)

Authors Information

E. Gwaltney
Department of Mathematics, Baylor University, Waco, Texas 76798, USA

P. Hagelstein
Department of Mathematics, Baylor University, Waco, Texas 76798, USA

D. Herden
Department of Mathematics, Baylor University, Waco, Texas 76798, USA

Citation Example

E. Gwaltney, P. Hagelstein, and D. Herden, A probabilistic proof of the Vitali Covering Lemma, Methods Funct. Anal. Topology 24 (2018), no. 1, 34-40.

BibTex

@article {MFAT1023,
AUTHOR = {E. Gwaltney and P. Hagelstein and D. Herden},
TITLE = {A probabilistic proof of the Vitali Covering Lemma},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {24},
YEAR = {2018},
NUMBER = {1},
PAGES = {34-40},
ISSN = {1029-3531},
MRNUMBER = {MR3783816},
URL = {http://mfat.imath.kiev.ua/article/?id=1023},
}

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