Show that (operatorname{supp}(u * w) subset overline{operatorname{supp} u+operatorname{supp} w},(A+B:={a+b: a in A, b in B})).
Question:
Show that \(\operatorname{supp}(u * w) \subset \overline{\operatorname{supp} u+\operatorname{supp} w},(A+B:=\{a+b: a \in A, b \in B\})\).
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Observe that the assertion is equivalent to saying suppu suppw C suppu w Assume that xo suppu suppw Since this is an open set there is some r 0 such that supp w we find x y suppu In B xo C suppu supp ...View the full answer
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