Let X be a random variable with distribution Pθ(θ ϵ Ω). Let W = {ωβ} be a set of null hypotheses, i.e., a set of subsets of Ω

**(Question#1: how can each null hypothesis be a subset of Ω, which seems to me to be a set of parameters of the distributions of X?)**, closed under intersection: ωi, ωj ϵ W implies ωi ∩ ωj ϵ W. For each ωβ let φβ(X) be a level α test. That is, prθ{φβ(X)=1} ≤ α for all θ ϵ ωβ

**(Question#2: Why is the test=1? I understood φβ(X) to be the test statistics, so why would the probability of it being 1 be less than α? Why 1, specifically?)**

I'd appreciate if anyone can guide me to the answers!