In this [paper][1] by Diaconis and Zabell from 1982, Theorem 2.1 and the remark after essentially stated that 
> Given two probability measures $P$ and $Q$ on the same probability space $\Omega$. If $Q\ll P$ and their
> RN-derivative $\frac{dQ}{dP} \in L^\infty$ , then $Q$ can be obtained from $P$ by conditioning.

The proof is very easy and the assumption $\frac{dQ}{dP} \in L^\infty$ is essential, I was wondering if it is possible to relax the assumption $\frac{dQ}{dP} \in L^\infty$ or if this is a necessary condition? I was looking at concrete cases of this problem, for example between $\text{Exp}(a)$ and $\text{Exp}(b)$.

I know very little about the literature on this topic, any suggestion is also appreciated. 





  [1]: https://statweb.stanford.edu/~cgates/PERSI/papers/zabell82.pdf