Brownian Sheet Images and Bessel–riesz Capacity
نویسنده
چکیده
We show that the image of a 2–dimensional set under d–dimensional, 2–parameter Brownian sheet can have positive Lebesgue measure if and only if the set in question has positive (d/2)–dimensional Bessel–Riesz capacity. Our methods solve a problem of J.-P. Kahane.
منابع مشابه
A pr 1 99 8 Brownian Sheet Images and Bessel – Riesz Capacity
We show that the image of a 2–dimensional set under d–dimensional, 2– parameter Brownian sheet can have positive Lebesgue measure if and only if the set in question has positive (d/2)–dimensional Bessel–Riesz capacity. Our methods solve a problem of J.-P. Kahane. Consider two independent d–dimensional Brownian motions X X(t) ; t 0 and Y Y (t) ; t 0. Let E 1 and E 2 denote two disjoint compact s...
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We show that the image of a 2{dimensional set under d{dimensional, 2{ parameter Brownian sheet can have positive Lebesgue measure if and only if the set in question has positive (d=2){dimensional Bessel{Riesz capacity. Our methods solve a problem of J.-P. Kahane.
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