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.

Full Text

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},
}

References

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