$\displaystyle m{\ast}A=0{\Rightarrow}m{\ast}(A{\cup}B)=m{\ast}B$
how can ı show this?
Hello,
$\displaystyle m{\ast}(A \cup B)+m {\ast}(A \cap B)=m{\ast}(A)+m{\ast}(B)$
but $\displaystyle m{\ast}(A \cap B) \leq m{\ast}(A)=0$ because $\displaystyle A \cap B \subseteq A$
Since a measure is always positive, $\displaystyle m{\ast}(A \cap B)=0$
Hence $\displaystyle m{\ast}(A \cup B)=m{\ast}(A)+m{\ast}(B)=m{\ast}(B)$