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Kelly’s theorem from the duality of LP and Tychonoff’s theorem. (English) Zbl 1008.28001
The authors give a new proof of Kelley’s theorem on the existence of a strictly positive probability charge on a Boolean algebra using the duality of Linear Programming and Tychonoff’s compactness theorem.
A posteriori comment from the editor: As cited in the paper an alternative proof using nonstandard analysis has been given by S.-A. Ng [Fundam. Math. 140, No. 1, 63–67 (1991; Zbl 0817.28003)].
Reviewer: Hans Weber (Udine)
MSC:
28A12 Contents, measures, outer measures, capacities
90C05 Linear programming
90C46 Optimality conditions and duality in mathematical programming
Citations:
Zbl 0817.28003
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References:
[1] BHASKARA RAO K. P. S.: Some important theorems in measure theory. Rend. Inst. Mat. Univ. Trieste 29 (1998), 81-113. · Zbl 0928.28001
[2] BHASKARA RAO K. P. S.-BHASKARA RAO M.: Theory of Charges. Academic Press, London-New York, 1983. · Zbl 0516.28001
[3] COTTLE R. W.-PANG JONG-SHI-STONE R. E: The Linear Complementarity Problem. Academic Press, London New York, 1992. · Zbl 0757.90078
[4] FREMLIN D. H.: Measure algebras. Handbook of Boolean algebras, Vol. III (J. Donald Monk, North-Holland, Amsterdam, 1989, pp. 887-980.
[5] KELLEY J. L.: Measures on Boolean algebras. Pacific J. Math. 9 (1959), 1165-1177. · Zbl 0087.04801
[6] SIU-AH, NG. : A new proof of Kelley’s theorem. Fund. Math. 140 (1991), 63-67. · Zbl 0817.28003
[7] WILHELM M.: Existence of additive functionals on semigroups and the Von Newmann minimax theorem. Colloq. Math. 35 (1976), 267-274. · Zbl 0328.20057
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