Brownian Sheet Images and Bessel-Riesz Capacity

Details Brownian Sheet Images and Bessel-Riesz Capacity Brownian Sheet Images and Bessel-Riesz Capacity

1998-04-10

arxiv.org/abs/math/9804061v1

Mathematics

Probability

19 pages

Scientific paper

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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