RIESZ s - EQUILIBRIUM MEASURES ON d - RECTIFIABLE SETS
نویسنده
چکیده
Let A be a compact set in Rp of Hausdorff dimension d. For s ∈ (0, d), the Riesz s-equilibrium measure μs is the unique Borel probability measure with support in A that minimizes Is(μ) := " 1 |x − y|s dμ(y)dμ(x) over all such probability measures. If A is strongly (Hd , d)-rectifiable, then μs converges in the weak-star topology to normalized d-dimensional Hausdorff measure restricted to A as s approaches d from below. Riesz potential, equilibrium measure, d-rectifiable
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تاریخ انتشار 2008