Radon-Nikodým derivatives for Banach lattice-valued measures

Author:
Ep de Jonge

Journal:
Proc. Amer. Math. Soc. **83** (1981), 489-495

MSC:
Primary 28B05; Secondary 46G10

MathSciNet review:
627676

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Abstract: Let be a measure space such that and such that has no -atoms. Furthermore, let be a Dedekind complete Banach lattice. By we denote the set of all -valued set functions on satisfying

(i) is additive,

(ii) is order bounded and of bounded variation,

(iii) is -absolutely continuous (with respect to the norm topology on ),

(iv) and satisfy

By we denote the set of -valued Bochner integrable functions on . It is shown that under the canonical map

Theorem. *Equivalent are*

(a) *is not isomorphic to a closed sublattice of* .

(b) *is isomorphic to an ideal in* .

Theorem. *Equivalent are*

(a) *is not isomorphic to a closed sublattice of* .

(b) *is isomorphic to* .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0627676-6

Keywords:
Radon-Nikodym derivatives,
Bochner integral,
Banach lattices

Article copyright:
© Copyright 1981
American Mathematical Society