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**Dilation for sets of probabilities.**
*(English)*
Zbl 0796.62005

A probability measure \(P\) is known to lie in a set of probability measures \(M\). Consider the probability of an event \(A\), \(P(A)\), which is known to lie in an interval \([\underline {P}(A), \overline{P}(A)]\). Then if this interval is contained in the interval \([\underline {P} (A| B), \overline{P}(A| B)]\) for every \(B\) in a partition \(\mathcal B\) then \(\mathcal B\) is said to dilate \(A\). Implications of dilation in robust Bayesian inference and the theory of upper and lower probabilities are studied and the conditions under which it occurs are investigated. Dilation immune neighbourhoods of the uniform measure are characterised.

Reviewer: P.W.Jones (Keele)