Electronic Resource
Springer
Manuscripta mathematica
13 (1974), S. 83-99
ISSN:
1432-1785
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract For a vector lattice E with the principal projection property, the following generalization of H.Freudenthal's spectral theorem is proved: There exists a measure space (Ω,R,π) such that integration with respect to π establishes a vector lattice isomorphism from L1(π) to E. Here π:ℛ→E is a σ -additive vector measure on some δ-ring R which, for [σ-] Dedekind complete E, may be chosen to be the δ-ring of relatively compact [Baire-] Borel sets in a locally compact space. Among others Kakutani's representation of abstract L-spaces as concrete L1 -spaces is an immediate consequence.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01168745
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