On the Fundamental Lemma of Neyman and Pearson

Abstract

The following lemma proved by Neyman and Pearson [1] is basic in the theory of testing statistical hypotheses: LEMMA. Let f1(x),⋯,fm+1(x) be m+1 Borel measurable functions defined over a finite dimensional Euclidean space R such that ∫R|fi(x)|dx