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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- Davar Khoshnevisan
- Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
- MR Author ID: 302544
- Email: email@example.com
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 2607-2622
- MSC (1991): Primary 60J45; Secondary 60G15
- DOI: https://doi.org/10.1090/S0002-9947-99-02408-3
- MathSciNet review: 1638246