24. The following example shows that Corollary 4 does not extend to a countably infinite family of distributions. Let Pn be the uniform probability density on [0, 1 + lin], and Po the uniform density on (0,1). (i) Then Po is linearly independent of (PI' P2'. . . ), that is, there do not exist constants CI' C2,' " such that Po = ECnPn· (ii) There does not exist a test IfJ such that flfJPn = a for n = 1,2, . . . but !l/Jpo> a.