Relationship between $m(E\backslash F) < \epsilon$ and $m(E)-m(F) < \epsilon$ This may be a fairly easy question but I just want to make sure there are no strange counterexamples.
Suppose $E$ and $F$ are measurable sets such that $F \subset E$. 
Now suppose $m(E \setminus F) < \epsilon$ Does this  imply that $m(E)-m(F) < \epsilon$ ?

Hint: $F\subset E$ implies $m(F)+m(E\backslash F)=m(E)$...
