A probabilistic proof of the Vitali Covering Lemma - Gwaltney, E.; Hagelstein, P.; Herden, D. (Methods of Functional Analysis and Topology, 2018)
The classical Vitali Covering Lemma on R states that there exists a constant c > 0 such that, given a finite collection of intervals {I_j} in R, there exists a disjoint subcollection {I_j} {I_j} such that |I_j| ≥ c |I_j|. We provide a new proof of this covering lemma using probabilistic techniques and Padovan numbers.