Set Function in semi algebra countably subadditive

Question

Let $\mu: C\rightarrow [0,+\infty]$ be a set function where $C$ is a semi algebra in $X$. If $\mu$ is subadditive

i.e. (If $B=\cup_{i\geq 1}A_i$ with $A_i, B$ in $C$ then $\mu(B)\leq \sum \mu(A_i)$)

Then $\mu$ is monotone?