Definition:Positive Set

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Definition

Let $\struct {X, \Sigma}$ be a measurable space.

Let $\mu$ be a signed measure on $\struct {X, \Sigma}$.

Let $A \in \Sigma$.


We say that $A$ is a $\mu$-positive set if and only if:

for each $E \in \Sigma$ with $E \subseteq A$ we have $\map \mu E \ge 0$.


Also see

  • Results about positive sets can be found here.


Sources