The interrelationships among conditions for convergence in law of sequences of likelihood ratios and the concept of contiguity are explored. Related results of Le Cam (1960), Hajek and Sidak (1967) and Roussas (1972) are extended, modified and clarified. In particular, it is shown that if likelihood ratios converge in law under the numerator hypothesis, then they converge under the denominator hypothesis and the hypotheses are contiguous (numerator to denominator).
"On the Concept of Contiguity." Ann. Probab. 5 (2) 278 - 282, April, 1977. https://doi.org/10.1214/aop/1176995851