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Let $(B_t,t\ge 0)$ be a linear Brownian motion and (L(t,x), t > 0, x ∈ ℝ) its local time. We prove that for all t > 0, the process (L(t,x), x ∈ [0,1]) belongs almost surely to the Besov-Orlicz space $B_{M_1,\infty }^{1/2}$ with $M_1\left(x\right)=e^{\left|x\right|}-1$.