Weak Conditional Independence and Relative Invariance in Bayesian Statistics

In this paper, the concept of invariance, standard in measure theory, is extended to the conditional case and is shown to provide a suitable framework to define invariant Bayesian experiments, even in the case of improper prior distributions. Also the concept of conditional independence, standard probability theory, is extended to the case of σ-finite (but unbounded) measures. both extensions require, as a preliminary step, to work out necessary conditions for the existence of a well defined "marginal conditional" decomposition (actually a desintegration) of a σ-finite measure. This framework is then used