Hagelstein, PaulGwaltney, EthanBaylor University.Daniel Herden2017-05-232017-05-232017-04-252017-05-23http://hdl.handle.net/2104/9937The Vitali Covering Lemma states that, given a finite collection of balls in R^d, there exists a disjoint subcollection that fills at least 3^{−d} of the measure of the union of the original collection. We present classical proofs of this lemma due to Banach and Garnett. Subsequently, we provide a new proof of this lemma that utilizes probabilistic “Erdo ̈s” type techniques and Padovan numbers.en-USBaylor University projects are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission.MathematicsThesisWorldwide access