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Brownian sheet images and Bessel-Riesz capacity

Author: Davar Khoshnevisan
Journal: Trans. Amer. Math. Soc. 351 (1999), 2607-2622
MSC (1991): Primary 60J45; Secondary 60G15
Published electronically: February 9, 1999
MathSciNet review: 1638246
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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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Additional Information

Davar Khoshnevisan
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
MR Author ID: 302544

Keywords: Capacity, Brownian sheet, additive Brownian motion, multi-parameter martingales.
Received by editor(s): September 23, 1997
Received by editor(s) in revised form: June 11, 1998
Published electronically: February 9, 1999
Additional Notes: Research supported by grants from the National Science Foundation and the National Security Agency
Article copyright: © Copyright 1999 American Mathematical Society