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{\bf Question}

$\cal C$ is a countable set.  Prove that for any set $S$,

$m^*(S\cup C)=m^*(S)$




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{\bf Answer}

$m^*(S\cup C)\leq m^*(S)+m^*(C)=m^*(S)$

But $S\subset S\cup C$  therefore $m^*(S)\leq m^*(S\cup C)$

Therefore $m^*(S)=m^*(S\cup C)$


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