We discuss conditions under which a convex cone K ⊂ RΩ admits a finitely additive probability m such that supk ∈ K m (k) ≤ 0. Based on these, we characterise those linear functionals that are representable as finitely additive expectations. A version of Riesz decomposition based on this property is obtained as well as a characterisation of positive functionals on the space of integrable functions. © 2009 Elsevier Inc. All rights reserved.
Cassese, G. (2009). Sure wins, separating probabilities and the representation of linear functionals. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 354(2), 558-563 [10.1016/j.jmaa.2009.01.013].
Sure wins, separating probabilities and the representation of linear functionals
CASSESE, GIANLUCA
2009
Abstract
We discuss conditions under which a convex cone K ⊂ RΩ admits a finitely additive probability m such that supk ∈ K m (k) ≤ 0. Based on these, we characterise those linear functionals that are representable as finitely additive expectations. A version of Riesz decomposition based on this property is obtained as well as a characterisation of positive functionals on the space of integrable functions. © 2009 Elsevier Inc. All rights reserved.
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