Formal posteriors for improper priors are investigated in connection with coherence, both in the sense of Regazzini and of Heath and Sudderth. Those priors $\pi$ which are linked with the improper prior $\gamma$ by the relation $\pi(B) = 0$ whenever $\gamma(B) < +\infty$ are studied in particular. Moreover, a characterization of the inferences which are coherent according to Heath and Sudderth is found, and several examples, exhibiting several phenomena, are given.
"Coherent Inferences and Improper Priors." Ann. Statist. 22 (3) 1177 - 1194, September, 1994. https://doi.org/10.1214/aos/1176325624