Under the assumptions of Theorem 9.2.1, suppose there exists another monotone rule E that strongly controls the FWER, and such that Pθ{dc 0,0} ≤ Pθ{e c

0,0} for all θ ∈ ωc 0,0 , (9.101)

with strict inequality for some θ ∈ ωc 0,0. Argue that the ≤ in (9.101) is an equality, and hence e0,0d0,0 has Lebesgue measure 0, where AB denotes the symmetric difference between sets A and B. A similar result for the region d1,1 can be made as well.