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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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


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
  • Email:
  • 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:
  • MathSciNet review: 1638246