If we take G = D′ the space of Schwartz distributions and want to characterize distributions which are locally functions, we must take for O(Ω) the classical function spaces called O′M(Ω) in the literature.
Then the projection on the first component of a distribution's wave front set is nothing else than its classical singular support, i.e. the complement of the set on which its restriction would be a smooth function.
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4 ... Next we have to scale the structures up by increasing m ...
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