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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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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Measures Integrals And Martingales

ISBN: 9781316620243

2nd Edition

Authors: René L. Schilling

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Question Posted: Jan 25, 2024 01:01 AM

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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

Measures Integrals And Martingales

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