I have been digging a little bit more on Mathematical Statistics on my own and came across the concept of Contiguity between two sequences of probability measures, all defined on the same measureable spaces:
Given a sequence of measureable spaces $(\Omega_n, \mathcal{F}_n)$ equipped with probability measures $P_n$ and $Q_n$, we say that the sequence of measures $\{Q_n\}$ is contiguous with respect to the sequence $\{P_n\}$ if, for any sequence of measureable sets $A_n$, it holds true that if $P_n(A_n) \rightarrow 0$ then $Q_n(A_n) \rightarrow 0$
Wikipedia article: https://en.wikipedia.org/wiki/Contiguity_(probability_theory)
This definition resembles the definition of absolutely continuou probability measures with respect to another measure, but in a sequential setting. Are there known results linking the two concepts? I couldn't find any although I believe that absolute continuity for every index $n$ implies contiguity, although it's only a conjecture from a starter in this field.
Thanks in advance!
If $(\Omega, \mathcal{F}) = (\Omega_n, \mathcal{F}_n)$, $P=P_n$, and $Q=Q_n$ for all $n$, then contiguity is equivalent to absolute continuity.
See this.