Coherent distributions and Lindley's paradox

A Bayesian test of a simple null hypothesis H_0 versus a composite alternative H_1 is performed using finitely additive prior distributions in order to investigate the so called Lindley's paradox. In particular two priors for the parameter under H_1 are considered. The first represents a coherently non-informative distributions which is shown to correctly yield the "paradox" because of the overall induced distribution of the parameter. The second, through the use of adherent masses the point specify by H_0, does instead avoid Lindley's paradox.