Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/101350
Authors: 
Khan, M. Ali
Rath, Kali P.
Year of Publication: 
2011
Series/Report no.: 
Working Papers, The Johns Hopkins University, Department of Economics 586
Abstract: 
We present proofs, based on the Shapley-Folkman theorem, of the convexity of the range of a strongly continuous, finitely additive easure, as well as that of an atomless, countably additive measure. We also present proofs, based on diagonalization and separation arguments respectively, of the closure of the range of a purely atomic or purely nonatomic countably additive measure. A combination of these results yields Lyapunov's celebrated theorem on the range of a countably additive measure. We also sketch, through a comprehensive bibliography, the pervasive diversity of the applications of the Shapley-Folkman theorem in mathematical economics.
Subjects: 
Strongly continuous measure
atomless measure
range of a measure
diagonalization argument
Hahn decomposition
Shapley-Folkman theorem
Lyapuonov's theorem
JEL: 
C07
D05
Document Type: 
Working Paper

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