Corollary 2
Tag 096I, permanent. Cite it as [Bourbaki, Tag 096I].
Integration, chapter V, § 7. Integration with respect to an induced measure
— Let θ be a complex measure on T, π a θ-proper mapping of T into a locally compact space Y, and π_X its restriction to X. Then π_X is θ_X-proper, and π_X(θ_X) = π(φ_X · θ).
For, π_X = π ∘ i, where i is the canonical injection X → T. When θ is positive the corollary may therefore be deduced from Prop. 3 and the transitivity of image measures (§6, No. 3, Prop. 4). The case of a non-positive complex measure then follows by linearity.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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