  It has recently been shown that the marginalization paradox (MP) can be
resolved by interpreting improper inferences as probability limits. The key to
the resolution is that probability limits need not satisfy the formal Bayes'
law, which is used in the MP to deduce an inconsistency. In this paper, I
explore the differences between probability limits and the more familiar
pointwise limits, which do imply the formal Bayes' law, and show how these
differences underlie some key differences in the interpretation of the MP.
