Here is the definition of meausrability of a set E given in my text:

It looks like (A∩(complement of E)) = (A~E) or (A\E) (just different notation)A setEis said to be measurable provided for any setA,m*(A) = m*(A∩E) + m*(A∩(complement of E))

So, the equation in the original problem looks very close to what I have in the definition of measurable set. Except I can't say it holds for any set A, only if A=(a,b).

If I were to restrict the measure space (correct term?) to one that contains the just open sets, then E would be measurable?

The complement of an measurable open set is a measurable closed set... What if I add these in?