By default, observation frames are finite, i.e., their sample spaces are finite.

The definition of observation frames should be more general by excluding $\Omega$ and dealing only with coobservation. But, at this initial point of our investigation, we are willing to sacrifice the generality. $\triangleleft$

Since every coobservable set is a subset of an ensemble and every subset of an ensemble is coobservable, the whole collection CO of coobservable event sets is determined by the ensembles.

Further, due to the finiteness proviso, the Boolean algebra of any ensemble $E$ is atomic. The atoms partition the sample space; let us call that partition $\Pi_E$. The partition $\Pi_E$ uniquely determines the ensemble $E$. Thus the collection CO can be given by the table of ensemble-induced partitions $\Pi_E$.

Piponi’s scenario gives rise to the following observation frame. The sample space $\Omega$ consists of the four binary strings $00, 01, 10, 11$, and there are three ensembles giving rise to the following partitions: $$\begin{aligned}
&\big\{\{00,01\},\{10,11\}\big\} \\ 
&\big\{\{00,10\},\{01,11\}\big\}\\   
&\big\{\{00,11\},\{01,10\} \big\}\end{aligned}$$

Furthermore, there is the least common refinement $\Pi$ of all the ensemble-induced partitions; it has the smallest number of parts. Notice that, for any part $e\in\Pi$, different outcomes in $e$ cannot be distinguished. For all 