Abstract
Let Ω be an open subset of Rd, d≥2, and let x∈Ω. A Jensen measure for x on Ω is a Borel probability measure μ, supported on a compact subset of Ω, such that ∫u dμ≤u(x) for every superharmonic function u on Ω. Denote by Jx(Ω) the family of Jensen measures for x on Ω. We present two characterizations of ext(Jx(Ω)), the set of extreme elements of Jx(Ω). The first is in terms of finely harmonic measures, and the second as limits of harmonic measures on decreasing sequences of domains.
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