Proposition 7

1° If A and B are two integrable sets such that $B \subset A$, then the set $C = A - B$ is integrable and

2° The intersection of a countable family of integrable sets is integrable.

The first part follows from the fact that $\varphi_C = \varphi_A - \varphi_B$. On the other hand, if $(A_n)$ is a sequence of integrable sets and $A$ is its intersection, then $\varphi_A = \inf_n \varphi_{A_n}$, therefore $A$ is integrable (No. 3, Prop. 4).