Brownian Sheet Images and Bessel-Riesz Capacity
arXiv:math/9804061
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.
19 pages