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Answer by Hannes for Is the measure density condition a necessary condition...
No, the measure density condition is not necessary I would say. Possibly there are more precise arguments, but I would argue as follows, in a nutshell: The desired inequality can be proven using...
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Let $\Omega \subseteq \mathbb{R}^M$ be a measurable subset of positive measure. R. A. Adams and J. Fournier in their article have proven that if $\Omega$ satisfies the so-called weak cone property,...
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