Most likely balls in Banach spaces: existence and non-existence

2023/09/06 by Schmidt, Bernd
#28C20 #60B11 #62F10 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2309.02846

Abstract

We establish a general criterion for the existence of convex sets of fixed shape as, e.g., balls of a given radius, of maximal probability on Banach spaces. We also provide counterexamples showing that their existence my fail even in some common situations.

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