Bourbaki

Corollary 4

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

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

Let I be a set and let (Hi)i∈I(H_i)_{i\in I} be a family of compact groups. The dual of the product group of the HiH_i is the discrete direct sum group of the groups H^i\widehat{H}_i.

This is a particular case of Corollary 3.

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.

Cited by

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Cites

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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.