The Bayesian analysis in Remark 1 c

The Bayesian analysis in Remark 1 can be obtained, if we assume that we have four variables: one takes values on Θ,
the other one takes values on 2X (the set of subsets of X), the third one is evidence E, and the fourth one is ω. It is also
assumed that E is independent of θ given X and ω, that the value Γ(ω) is obtained with probability 1 given ω and E,
and that given A ⊆ X, the probability of θ is equal to PX(A|θ) . Under these conditions, the analysis in the paper provides PX(A)
the result of Eq. (42) in Denœux’s paper [1]. However, these assumptions are not quite natural: first it has been necessary
to transform X into 2X. The conditional information on Θ given A has been computed with the original probabilistic information, however not all the original specifications have been taken into account. If in this model we compute the
probability P(A|θ), what is obtained is that this probability is proportional to m (A)