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

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Condition on Functions on Overlapping patches of a Domain

Let $\Omega\subset \mathbb{R}^n$ be a bounded domain. Let $\{p_i\}_{i=1}^m$ for some finite $m\in\mathbb{N}$ be the overlapping open sets of $\Omega$ such that $\Omega =\bigcup_{i=1}^mp_i$. Now, Defin …