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On the Hausdorff measure for a trajectory of a Brownian motion in l_2

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Abstract

We consider the Hausdorff measure for Brownian motion(BM) in l_2.Several path properties of BM in l_2 are used to show the upperbound of Hausdorff measure. We also show the lower bound of itapplying a law of iterated logarithm for the occupation time of BM in l_2.

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