=+12.3. 1 If A € .91 and A(A) > 0, then the origin is interior to the difference set D(A) =[x-y: x, y = A]. Hint: Choose a bounded open interval / as in Problem 12.2 for 0 = 2. Suppose that |z| < A(/)/2; since ANI and (ANI) +z are contained in an interval of length less than 3A(1)/2 and hence cannot be disjoint, z € D( A).