Robert Kaufman’s proof that the set of rapid points of Brownian motion has a Fourier dimension equal to its Hausdorff dimension was first published in 1974. A study of the proof of the original paper revealed several gaps ...
Using Loeb measure theory, it is possible to construct Lebesgue or even Wiener measure as a hyperfinite counting measure. In this paper I explore an extension of the idea to Hausdorff measure, which yields a hyperfinite ...
By considering a counting-type argument on Brownian sample paths, we prove
a result similar to that of Orey and Taylor on the exact Hausdorff dimension of the rapid
points of Brownian motion. Because of the nature of the ...