Abstract
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.
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