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Let $n$ be the spatial dimension. For $d$, $0<d\leq n$, let $H^{d}$ be the $d$-dimensional Hausdorff content. The purpose of this paper is to prove the boundedness of the dyadic strong maximal operator on the Choquet space $L^{p}(H^{d},\R^n)$ for $\min(1,d)<p$. We also show that our result is sharp.
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