Remark 1
Tag 09FS, permanent. Cite it as [Bourbaki, Tag 09FS].
Integration, VII, p. 42, § 2. Quotient of a space by a group; homogeneous spaces
One deduces from Remark 1 of No. 3 that the nonzero quasi-invariant measures on G/H are none other than the pseudo-images under of a Haar measure on G.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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