Proposition 1

Tag 09LZ, permanent. Cite it as [Bourbaki, Tag 09LZ].

The set $\Gamma$ is closed in the space $\mathscr{M}_+(G) - \{0\}$ equipped with the vague topology. We first prove the following lemmas:

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

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