suppose A,B is nonmeasurable. Hence A,B both have nonzero outermeasure (note: outermeasure exists for every subset of R). Assume AxB is measurable. Let C(x)={y in R: (x,y) is in AxB}, C(x)=the empty set if x is not in A, C(x)=B if x is in A. Let D={x in R: C(x) is nonmeasurable}. By Cavalieri's...