While reading "On computability and disintegration" by N. Ackerman, C. Freer, D. Roy, I encountered the following statement (page 7):
"every point of continuity of an absolutely continuous distribution is a Tjur point"
that I do not know how to interpret. While I am accustomed to the measure-theoretic jargon, it seems that the above uses some terminology from statistics, a field that I have absolutely no idea of.
Could somebody fluent in both measure theory and statistics translate the above in measure-theoretic terms, please?
In particular, does "point of continuity" mean a point of measure $0$? And what is an "absolutely continuous distribution"? I only know of absolutely continuous measure with respect to another measure, in the context of the Radon-Nikodym theorem, but it seems that the expression has a different use here.