• Corpus ID: 251402960

Partial reconstruction of measures from halfspace depth

  title={Partial reconstruction of measures from halfspace depth},
  author={Petra Laketa and Stanislav Nagy},
. The halfspace depth of a d -dimensional point x with respect to a finite (or probability) Borel measure µ in R d is defined as the infimum of the µ -masses of all closed halfspaces containing x . A natural question is whether the halfspace depth, as a function of x ∈ R d , determines the measure µ completely. In general, it turns out that this is not the case, and it is possible for two different measures to have the same halfspace depth function everywhere in R d . In this paper we show that… 

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