Remark

Tag 09SA, permanent. Cite it as [Bourbaki, Tag 09SA].

Integration, chapter IX, § 6. Promeasures and measures on a locally convex space

— When $E$ is finite-dimensional, every character of $E$ is of the form $x \mapsto e^{i\langle x, x' \rangle}$ with $x' \in E'$ (Théor. spect., Ch. II, §1, No. 9, Cor. 3 of Prop. 12). In this case, Prop. 3 follows from the uniqueness theorem for the Fourier transformation (loc. cit., §1, No. 6, Cor. of Prop. 6).*

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Prop. 3