$e\in E$, whether $e$ occurred or not. Further, $e$ is observable if the singleton set $\{e\}$ is coobservable.

An *observation frame* is a pair $(\Omega,{\ensuremath{\mathrm{CO}}})$, such that $\Omega$ is a nonempty set, CO is a collection of subsets of $\Omega$, and the following axioms hold:

-    If $X\subseteq Y\in{\ensuremath{\mathrm{CO}}}$ then $X\in{\ensuremath{\mathrm{CO}}}$.

-    If $e_1,e_2\in X\in{\ensuremath{\mathrm{CO}}}$ then $X\cup\{\overline{e_1}\}\in{\ensuremath{\mathrm{CO}}}$ and $X\cup\{e_1\cup e_2\}\in{\ensuremath{\mathrm{CO}}}$. $\triangleleft$

Event sets in CO are *coobservable*. An event $e$ is *observable* if the set $\{e\}$ is coobservable. For brevity, maximal coobservable sets, maximal in the inclusion order, will be called *ensembles*. $\triangleleft$

The set $\bigcup{\ensuremath{\mathrm{CO}}}$ of the observable events will be denoted Ob.

It follows from the definition that every ensemble is a Boolean algebra of subsets of $\Omega$.

> [[Q: ]{}]{}How do you justify CO2.
>
> [[A: ]{}]{}Let $e_1,e_2\in X\in{\ensuremath{\mathrm{CO}}}$. Since $X$ is coobservable, there exists a test $\tau_X$ that allows us to observe, for all $e\in X$, whether $e$ occurred or not. Therefore $\tau_X$ also allows us to observe whether $\overline{e_1}$ occurred or not: it occurred if and only if $e_1$ didn’t occur. And $\tau_X$ allows us to observe whether $e_1\cup e_2$ occurred or not: it occurred if and only if $e_1$ occurred or $e_2$ occurred.

