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},
}
