On the equivalence of invariance and almost-invariance from a bayesian point of view

This paper contains several results and examples about the equivalence (including equivalence in a weaker sense of the usual one) of the invariant and almost - invariant s-fields in a Bayesian statistical experiment and the equivalence of their intersections with a sufficient s-fields. This last equivalence is used in a classical setting in the well known paper Hall, Wijsman, Ghosh (1965) to prove the main theorem