In this chapter we shall consider a double sequence \(\lbrace{\mathcal{E}_{n,j}; j = {\text{1,2}},\dotsb; n = {\text{1,2}}, \dotsb \rbrace}\) of experiments \(\mathcal{E}_{n,j} = \lbrace{p_{t,n,j}; t \in \Theta\rbrace}\) indexed by the same set Θ. Let ℇ n be the direct product of the \(\mathcal{E}_{n,j}; j = {\text{1,2}},\dotsb.\). That is, ℇ n consists of performing the \(\mathcal{E}_{n,j}; j = {\text{1,2}},\dotsb\) independently of one another. We shall assume generally, that for each integer n, the ℇ n,j are trivial from some j n on. The measures constituting ℇ n are the product measures \(P_{t,n} = \Pi_j p_{t,n,j}\), with t Є Θ. We propose, as our illustration of the arguments of Chapter 3, to study the limiting behavior of likelihood ratios of the type \(\Lambda_n = log\frac{dP_{1,n}}{dP_{0,n}}\) where 0 and 1 are names for possible values of the parameter t Є Θ. (Most of the arguments will be carried out for the case of binary experiments \(\mathcal{E}_n = (P_{0,n},P_{1,n})\) but more general situations will also be mentioned.