Remark 1
Tag 09L0, permanent. Cite it as [Bourbaki, Tag 09L0].
Integration, VIII, p. 44, § 4. Convolution of measures and functions
We thus see that every measure on is the limit of measures admitting a continuous density with respect to every Haar measure (for the topology indicated in Prop. 19 and a fortiori for the vague topology).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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