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A Yosida–Hewitt decomposition for totally monotone games

2003; Elsevier BV; Volume: 48; Issue: 1 Linguagem: Inglês

10.1016/j.mathsocsci.2003.10.002

1879-3118

Alain Chateauneuf, Yann Rébillé,

Logic, Reasoning, and Knowledge

We first prove for totally monotone games defined on the set P(N) of the subsets of N, a similar decomposition theorem to the famous Yosida–Hewitt's one for finitely additive measures. As a byproduct we both derive for σ-continuous belief functions on P(N) a natural and simple generalization of the Möbius inverse and of a related tractable formula for the Choquet integral.