Let (left(E_{j}ight)_{j geqslant 1}) be subsets of (mathbb{R}^{d}) and (E:=bigcup_{j geqslant 1} E_{j}). Show that (operatorname{dim} E=sup
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Let \(\left(E_{j}ight)_{j \geqslant 1}\) be subsets of \(\mathbb{R}^{d}\) and \(E:=\bigcup_{j \geqslant 1} E_{j}\). Show that \(\operatorname{dim} E=\sup _{j \geqslant 1} \operatorname{dim} E_{j}\).
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