Theorem 3

Tag 0C97, permanent. Cite it as [Bourbaki, Tag 0C97].

Let $X$ be a Lusin space. Then a subspace of $X$ is a Lusin space if and only if it is a Borel set.

This theorem is a consequence of the following two lemmas:

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

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