On the jordan decomposition for vector measures
It is shown that a vector measure μ on an algebra of sets with values in an order complete Banach lattice G is the difference of two positive vector measures if either μ is bounded and G is an order complete AM-space with unit, or μ has bounded variation and there exists a positive contractive projection G" → G. This result is a complete counterpart to the corresponding one on the regularity of a bounded linear operator.
KeywordsLinear Operator Vector Lattice Bounded Linear Operator Bounded Variation Banach Lattice
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