Definition 4

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

Integration, chapter IV, § 5. Measurable functions and sets

— Given a locally compact subspace Y of a locally compact space X, we call measure induced on Y by a measure $\mu$ on X, and denote by $\mu_Y$ or $\mu|Y$ , the measure defined by the formula

\int g \, d\mu_Y = \int g' \, d\mu

for every function $g \in \mathscr{K}(Y; \mathbf{C})$ , where $g'$ denotes the function equal to $g$ on $Y$ and to 0 on $X - Y$ .

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

Cited by

Example, § 5
§ 1. Premeasures and measures on a topological space

Cites

Nothing.