Corollary

Tag 09T3, permanent. Cite it as [Bourbaki, Tag 09T3].

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

— Let F be a barreled nuclear space; equip F' with a locally convex topology $\mathscr{T}$ intermediate to the weak topology $\sigma(F', F)$ and the topology of uniform convergence on the compact convex subsets of F. The Fourier transformation is a bijection of the set of bounded (positive) measures on F' onto the set of continuous functions of positive type on F.

This follows immediately from Theorem 4 and the Cor. of Th. 2 of No. 10.*

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

Cited by

Nothing.

Cites

Cor. of Th. 2
Theorem 4