Abstract
Let (Ω
, νi) be a probability space for i=1,2 with
and ϕ:Ω ⇒ ℝm a correspondence, i.e. ϕ(ω) is a non-void subset of ℝm for all ω∈Ω. We give necessary and sufficient conditions under which it holds, that ν2 extends ν1. iff ∫A ϕ dν2 is equal to ∫A ϕ dν1 for all A∈
, where ∫Aϕ dνi is the set of all integrals ∫A f dνi of functions f: Ω → ℝm with f(ω)∈ϕ(ω) νi.-a.e.
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Rupp, W. Mengenwertige Masse und Fortsetzungen. Manuscripta Math 22, 137–150 (1977). https://doi.org/10.1007/BF01167857
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DOI: https://doi.org/10.1007/BF01167857