Definition 2

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

Integration, chapter II, § 2. Linear forms on a Riesz space

Given a Riesz space $E$ , a linear form $L$ on $E$ is said to be relatively bounded if, for every $x \geqslant 0$ in $E$ , $L$ is bounded on the set of $y \in E$ such that $|y| \leqslant x$ .

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

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