In this paper, I provide a characterization of a \textit{set} of probability
measures with which a prior ``weakly merges.'' In this regard, I introduce
the concept of ``conditioning rules'' that represent the \textit{regularities%
} of probability measures and define the ``eventual generation'' of
probability measures by a family of conditioning rules. I then show that a
set of probability measures is learnable (i.e., all probability measures in
the set are weakly merged by a prior) if and only if all probability
measures in the set are eventually generated by a \textit{countable} family
of conditioning rules. I also demonstrate that quite similar results are
obtained with ``almost weak merging.'' In addition, I argue that my
characterization result can be extended to the case of infinitely repeated
games and has some interesting applications with regard to the impossibility
result in Nachbar (1997, 2005).