On consistency of Bayes procedures

For a wide class of statistical models with $\sigma$-finite priors, sufficient conditions for consistency of Bayes procedures for almost all values of the parameter are given. For a more restrictive class of invariant statistical models with some $\sigma$-finite priors, we give sufficient conditions for consistency of Bayes procedures for all values of the parameter. Particular cases of these invariant statistical models include the location model on a locally compact Polish group, rotation invariant families on the unit sphere in $\mathbf{R}^k$, and the scale-location model in $\mathbf{R}^k$.