Let $V({}^\ast{X})$ be an enlargement of ${}^{\ast}{V(X)}$ and $C$ be a fixed internal set in $V({}^\ast{X})$. $\{A_k\}_{k \in \Bbb N}$ is strictly increasing sequence of internal subsets of $C$. It is known that $\bigcup_{k \in \Bbb N} A_k$ must be external by countable saturation property.
But why this implies that the standard part of an internal finitely additive measure on an internal algebra is alway $\sigma$-additive?