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Brownian sheet images and Bessel-Riesz capacity
Author(s):
Davar
Khoshnevisan
Journal:
Trans. Amer. Math. Soc.
351
(1999),
2607-2622.
MSC (1991):
Primary 60J45;
Secondary 60G15
Posted:
February 9, 1999
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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:
10.1090/S0002-9947-99-02408-3
PII:
S 0002-9947(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
Posted:
February 9, 1999
Additional Notes:
Research supported by grants from the National Science Foundation and the National Security Agency
Copyright of article:
Copyright
1999,
American Mathematical Society
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