Abstract
We show that if $2N \leq d$, then with probability 1 the Brownian sheet $W: R^N_+ \rightarrow R^d$ satisfies $\forall$ Borel set $E, \dim W(E) = 2 \dim E$.
Citation
T. S. Mountford. "Uniform Dimension Results for the Brownian Sheet." Ann. Probab. 17 (4) 1454 - 1462, October, 1989. https://doi.org/10.1214/aop/1176991165
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