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On the Sobolev removability of the graph of one-dimensional Brownian motion (2312.07270v1)
Published 12 Dec 2023 in math.PR and math.MG
Abstract: Suppose that $B$ is a one-dimensional Brownian motion and let $\Gamma = { (t, B_t) : t \in [0,1]}$ be the graph of $B|_{[0,1]}$. We characterize the Sobolev removability properties of $\Gamma$ by showing that $\Gamma$ is almost surely not $W{1,p}$--removable for all $p \in [1, \infty)$ but is almost surely $W{1,\infty}$--removable.
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