Question: 5. If the sample space !l is Euclidean and Po, PI have densities with respect to Lebesgue measure, there exists a nonrandomized most powerful test

5. If the sample space !l is Euclidean and Po, PI have densities with respect to Lebesgue measure, there exists a nonrandomized most powerful test for testing Po against PI at every significance level a.· [This is a consequence of Theorem 1 and the following lemma.' Let f 0 and fAf(x) dx =

a. Given any 0 b

a, there exists a subset B of A such that fBf(x) dx = b.]

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