## The Jordan decomposition of vector-valued measures

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- by B. Faires and T. J. Morrison PDF
- Proc. Amer. Math. Soc.
**60**(1976), 139-143 Request permission

## Abstract:

This paper gives criteria for a vector-valued Jordan decomposition theorem to hold. In particular, suppose*L*is an order complete vector lattice and $\mathcal {A}$ is a Boolean algebra. Then an additive set function $\mu :\mathcal {A} \to L$ can be expressed as the difference of two positive additive measures if and only if $\mu (\mathcal {A})$ is order bounded. A sufficient condition for a countably additive set function with values in ${c_0}(\Gamma )$, for any set $\Gamma$, to be decomposed into difference of countably additive set functions is given; namely, the domain being the power set of some set.

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## Additional Information

- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**60**(1976), 139-143 - MSC: Primary 28A45; Secondary 46G10
- DOI: https://doi.org/10.1090/S0002-9939-1976-0419723-X
- MathSciNet review: 0419723