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
- 2013: Donald L. Cohn: Measure Theory (2nd ed.) ... (previous) ... (next): $4.1$