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Browsing by Author "Potgieter, Paul"

Browsing by Author "Potgieter, Paul"

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  • Potgieter, Paul (Springer, 2013)
    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 ...
  • Potgieter, Paul (2009-08)
    After an introduction to Brownian motion, Hausdorff dimension, nonstandard analysis and Loeb measure theory, we explore the notion of a nonstandard formulation of Hausdorff dimension. By considering an adapted form of the ...
  • Potgieter, Paul (2009-03)
    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 ...
  • Potgieter, Paul (2012)
    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 ...

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