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

DOI:
https://doi.org/10.1090/S0002-9947-99-02408-3

Published electronically:
February 9, 1999

MathSciNet review:
1638246

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the image of a 2-dimensional set under -dimensional, 2-parameter Brownian sheet can have positive Lebesgue measure if and only if the set in question has positive ()-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

Email:
davar@math.utah.edu

DOI:
https://doi.org/10.1090/S0002-9947-99-02408-3

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