MathSciDoc: An Archive for Mathematician ∫

Let Ω be an open subset of$R$^{$d$},$d$≥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$$d$μ≤$u$($x$) for every superharmonic function$u$on Ω. Denote by$J$_{$x$}(Ω) the family of Jensen measures for$x$on Ω. We present two characterizations of ext($J$_{$x$}(Ω)), the set of extreme elements of$J$_{$x$}(Ω). The first is in terms of finely harmonic measures, and the second as limits of harmonic measures on decreasing sequences of domains.

No keywords uploaded!