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{\bf Question}

$A$ is a measurable set, and $S$ is a subset of $A$ of measure
zero.  Is $A-S$ necessarily measurable?  Justify your assertion.



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{\bf Answer}

$A\epsilon{\cal M}$

Since $m^*(S)=0, \,\,\, S\epsilon{\cal M}$

Therefore $A-S\epsilon{\cal M}$




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