Corollary 1
Tag 096H, permanent. Cite it as [Bourbaki, Tag 096H].
Integration, chapter V, § 7. Integration with respect to an induced measure
— If X is closed, then every complex measure on X is induced by a measure on T.
For, if K is a compact set in T then K ∩ X is compact, hence λ-integrable.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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