Let {} be a class of mutually exclusive sets of alternatives such that the envelope power function

Let {Ω∆} be a class of mutually exclusive sets of alternatives such that the envelope power function is constant over each Ω∆ and that

∪Ω∆ = Ω − ΩH, and let ϕ∆ maximize the minimum power over Ω∆. If ϕ∆ = ϕ

is independent of ∆, then ϕ is most stringent for testing θ ∈ ΩH.