Abstract
The space L w 1 ( ν ) of all scalarly integrable functions with respect to a Fréchet-space-valued vector measure ν is shown to be a complete Fréchet lattice with the σ -Fatou property which contains the (traditional) space L 1 ( ν ) , of all ν -integrable functions. Indeed, L 1 ( ν ) is the σ -order continuous part of L w 1 ( ν ) . Every Fréchet lattice with the σ -Fatou property and containing a weak unit in its σ -order continuous part is Fréchet lattice isomorphic to a space of the kind L w 1 ( ν ) .
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