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Integral representation without additivity
Open accessAbstract
Let I be a norm-continuous functional on the space B of bounded Σ -measurable real valued functions on a set S , where Σ is an algebra of subsets of S . Define a set function v on Σ by: v ( E ) equals the value of I at the indicator function of E . For each a in B let \[ J ( a ) = ∫ − ∞ 0 ( v ( a ≥ α ) − v ( S ) ) d α + ∫ 0 ∞ v ( a ≥ α ) d α . \] Then I = J on B if and only if I ( b + c ) = I ( b ) + I ( c ) whenever ( b ( s ) − b ( t ) ) ( c ( s ) − c ( t ) ) ⩾ 0 for all s and t in S .
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Cites
Choquet, G. (1954) · Annales de l'Institut Fourier · doi:10.5802/aif.53 · Cited by 4,204
Shapley, L. S. (1971) · International Journal of Game Theory · doi:10.1007/bf01753431 · Cited by 1,613
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Metadata
- Authors
- Schmeidler, D.
- Venue
- Proceedings of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Published
- 1986
- Volume
- 97
- Issue
- 2
- Pages
- 255-261
- ISSN
- 0002-9939 (ISSN-L)
- 1088-6826
- OpenAlex
- W2020154669
- Cited by
- 933
- References
- 2
- FWCI
- 5.16
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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