Brownian sheet images and Bessel-Riesz capacity

Khoshnevisan, Davar

doi:10.1090/S0002-9947-99-02408-3

Brownian sheet images and Bessel-Riesz capacity
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by Davar Khoshnevisan PDF

Trans. Amer. Math. Soc. 351 (1999), 2607-2622 Request permission

Abstract:

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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