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Let $H^d$, $0<d<n$, be the dyadic Hausdorff content of the $n$-dimensionalEuclidean space ${\mathbb R}^n$. It is shown that $H^d$ counts a~Cantor set ofthe unit cube $[0, 1)^n$ as $\approx 1$, which implies unboundedness of thesparse operator ${\mathcal A}_{{\mathcal S}}$ on the Choquet space ${\mathcalL}^p(H^d)$, $p>0$. In this paper we verify that the sparse operator ${\mathcalA}_{{\mathcal S}}$ maps ${\mathcal L}^p(H^d)$, $1\le p<\infty$, into anassociate space of Orlicz-Morrey space ${{\mathcal M}^{p'}_{\Phi_0}(H^d)}'$,$\Phi_0(t)=t\log(e+t)$. We also give another characterizations of thoseassociate spaces using the tiling ${\mathcal T}$ of ${\mathbb R}^n$.

Choquet integrals, Hausdorff content and sparse operators