Riesz s-equilibrium measures on d-dimensional fractal sets as s approaches d
نویسندگان
چکیده
منابع مشابه
RIESZ s - EQUILIBRIUM MEASURES ON d - RECTIFIABLE SETS
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...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2010
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2010.05.061