Realization of every measure in \mathfrak{P} by the cited theorem

Let $\mathfrak{P}$ be the set of measures considered in the paper that arise directly or indirectly, after extension, from a Markov stopping time, and let Theorem~ be the cited construction theorem. Realization conjecture. Every measure $\mu$ in the set $\mathfrak{P}$ can be obtained using Theorem~. The surrounding discussion presents this as an unresolved question about whether all measures in $\mathfrak{P}$ arise from the measures covered by the cited theorem.