Proposition 3

Tag 08MW, permanent. Cite it as [Bourbaki, Tag 08MW].

Integration, III, p. 26, § 2. Support of a measure

If $\mu$ and $\nu$ are two measures on a locally compact space $X$ such that $|\mu| \leq |\nu|$ , then $\mathrm{Supp}(\mu) \subset \mathrm{Supp}(\nu)$ .

For, if the restriction of $\nu$ to an open set is zero, then so is that of $\mu$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

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Cites

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