 Positive linear functional

A linear functional $\Lambda$ on an ordered vector space of functions is positive when $f\ge 0$ implies $\Lambda (f)\ge 0$. Positivity implies monotonicity: $f\le g$ gives $\Lambda (f)\le \Lambda (g)$.

A **positive linear functional** is a specific type of linear functional in the context of functional analysis, which is a branch of mathematics that studies vector spaces and linear operators.