On the Savage-Dickey paradox

Following several posts on this topic, we eventually managed to write down a short note with Jean-Michel Marin, which is now posted on arXiv, waiting for a last round of polishing before being submitted to the Annals. My conclusion on this topic is that Dickey’s (1971) condition on the conditional prior under the alternative has no measure-theoretic meaning unless additional continuity conditions are imposed upon those priors, while the other choices of versions found in the derivation can be seen as imposing a representation of

that holds everywhere instead of almost everywhere.