Bourbaki

Definition 4

Tag 02IF, permanent. Cite it as [Bourbaki, Tag 02IF].

Théories spectrales, chapter II, § 1. Transformation de Fourier

The Haar measure ν\nu on G^\widehat{G} of proposition 9 is called the dual measure of the given Haar measure dxdx on G.

We shall often denote by dχd\chi or dx^d\widehat{x} the Haar measure on G^\widehat{G} which is dual to the Haar measure dxdx.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

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Machine translation of the English, by gpt-5.4, gpt-5-6-mini, against glossary version 34. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.