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- Thread starter OB1
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in [itex]\mathbb{R}^n[/itex], you will not find any set that has a dimension [itex]>n[/itex] !! To construct a set with Hausdorf dimension [itex]0 < d < n[/itex], it suffices to construct a set [itex]E[/itex] that has a [itex]d[/itex]-Hausdorf measure [itex]0 < \mathcal{H}^{(d)}(E) < \infty[/itex]. If you know the example of Cantor-like sets in [itex]\mathbb{R}[/itex], you can adapt the idea in [itex]\mathbb{R}^n[/itex].

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