For every (B subset mathbb{R}^{n}) one has (operatorname{dim}_{mathcal{H}} B leqslant n). If (B) contains an open set

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For every \(B \subset \mathbb{R}^{n}\) one has \(\operatorname{dim}_{\mathcal{H}} B \leqslant n\). If \(B\) contains an open set or a set of strictly positive Lebesgue measure, then \(\operatorname{dim}_{\mathcal{H}} B=n\).

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