If $A$ and $B$ are measurable sets with $\mu(A) < \mu(B)$ , and $P \subset A$ , $Q \subset B$ are measurable sets with $\mu(P) = \mu(Q)$, is it true that $\mu(A-P) < \mu(B-Q)$? It seems this should be true intuitively, but I am not sure about the proof.