let $\mu: S \to \mathbb{R} $ be a finite additive measure defined on the semiring $S$.
Let $B(S) = $ {$A \subseteq \Omega$ | $A$ or $ A^{\mathsf{c}}$ $\in A(S)$ }
$A(S)$ is the ring constructed by disjoint unions of the semiring $S$ (minimal Ring)
1) Show that $B(S)$ is an algebra (contains $\Omega $ and contains $B^\mathsf{c}$, for all B $\in$ $B(S)$.
2)If $A(S)$ is not an algebra, so given any t $\in$ $[-\infty,+\infty]$ show that there is a unique finitelly additive measure $\mu_t : B(S) \to \mathbb{R} \cup $ {$t$} extending $\mu$ such that $\mu_t$ ($\Omega$)= t
3) If $\mu$ is $\sigma$-additive and $\Omega$ $\notin$ { $\cup_{i=1}^\infty S_n$ | $S_n$ $\in S$}, so $\mu_t$ is $\sigma$-additive
I already thank you who get involved with the problem .