Definition:Hahn Decomposition

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

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

We say that $\tuple {P, N}$ is a Hahn decomposition of $\mu$ if and only if:

$(1): \quad$ $P$ and $N$ are disjoint.
$(2): \quad$ $X = P \cup N$
$(3): \quad$ $P$ is $\mu$-positive and $N$ is $\mu$-negative.

Also see

Source of Name

This entry was named for Hans Hahn.