Example

Tag 08LH, permanent. Cite it as [Bourbaki, Tag 08LH].

Integration, chapter III, § 1. Measures on a locally compact space

Lebesgue measure on $\mathbf{R}$ is invariant under every translation of the additive group $\mathbf{R}$ . Indeed, for every function $f \in \mathscr{K}(\mathbf{R}; \mathbf{C})$ and every real number $a$ , we have

\int_{-\infty}^{+\infty} f(x + a)\, dx = \int_{-\infty}^{+\infty} f(t)\, dt

by the change-of-variables formula (FRV, II, §2, No. 1, formula (1)). For a generalization, see Ch. VII, §1, No. 2, Th. 1.

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

Cited by

Nothing.

Cites

FRV, II, §2, No. 1 not yet on this site: FVR II
VII, §1, No. 2, Th. 1