Definition:Negative Part of Signed Measure
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Definition
Let $\struct {X, \Sigma}$ be a measurable space.
Let $\mu$ be a signed measure on $\struct {X, \Sigma}$.
Let $\tuple {\mu^+, \mu^-}$ be the Jordan decomposition of $\mu$.
We say that $\mu^-$ is the negative part of $\mu$.
Sources
- 2013: Donald L. Cohn: Measure Theory (2nd ed.) ... (previous) ... (next): $4.1$