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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

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Minimal condition on set for an optimisation problem

We fix $\Omega \subset \mathbb{R}^{2}$ an open set. My question is: what are the minimum conditions we need on $E \subset \Omega$ such that the following optimisation problem: $$ \sup\{ \int_{E}(\part …
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