Georgia Institute of Technology College of Sciences

We will finish our proof of the key lemma for the probabilistic unique continuation principle used in Ding-Smart. We will also briefly recall enough of the theory of martingales to clarify a use of Azuma's inequality, and the basic definitions of \epsilon-nets and \epsilon-packings required to formulate the basic volumetric bound for these in e.g. the unit sphere, before using these to complete the proof.