An F-quantum space is a set \(M\subset [0,1]^ X\) such that (i) \(1\in M\); (ii) if \(a\in M\), then \(a^{\perp}=1-a\in M;\) (iii) 1/2\(\not\in M\); \((iv)\quad \cup^{\infty}_{i}f_ i:=\sup f_ i\in M.\) A subset A of M is commensurable if there is a Boolean algebra B in M containing A; we recall that a Boolean algebra B is a subset of M such that there are a maximal and a minimal element, \(1_ B\) and \(0_ B\), respectively, of B, with \(0_ B\leq a\leq 1_ B\) and \(a\vee a^{\perp}=1_ B\) for any \(a\in B\). It is shown that A is commensurable iff \(a\vee a^{\perp}=b\vee b^{\perp}\) for all a,b\(\in A\). Some applications to simultaneous measurement of observables are given.