A probabilistic proof of the Vitali Covering Lemma

Authors

  • 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 

DOI:

Keywords:

Differentiation of integrals, covering lemmas, probabilistic method

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.

Downloads

Published

2018-03-25

Issue

Vol. 24 No. 1 (2018)

Section

Articles

How to Cite

Gwaltney, E., et al. “A Probabilistic Proof of the Vitali Covering Lemma”. Methods of Functional Analysis and Topology, vol. 24, no. 1, Mar. 2018, pp. 34-40, https://zen.imath.kiev.ua/index.php/mfat/article/view/682.