Thus the notion of contiguity extends the concept of absolute continuity to the sequences of measures.
The concept was originally introduced by Le Cam (1960) as part of his foundational contribution to the development of asymptotic theory in mathematical statistics.
He is best known for the general concepts of local asymptotic normality and contiguity.
The notion of contiguity is closely related to that of absolute continuity.
That is, Q is absolutely continuous with respect to P if the support of Q is a subset of the support of P, except in cases where this is false, including, e.g., a measure that concentrates on an open set, because its support is a closed set and it assigns measure zero to the boundary, and so another measure may concentrate on the boundary and thus have support contained within the support of the first measure, but they will be mutually singular.
In summary, this previous sentence's statement of absolute continuity is false.
The contiguity property replaces this requirement with an asymptotic one: Qn is contiguous with respect to Pn if the "limiting support" of Qn is a subset of the limiting support of Pn.
It is possible however that each of the measures Qn be absolutely continuous with respect to Pn, while the sequence Qn not being contiguous with respect to Pn.
A similar result exists for contiguous sequences of measures, and is given by the Le Cam's third lemma.
Le Cam's first lemma shows that the properties of the associated limit points determine whether contiguity applies or not.
This can be understood in analogy with the non-asymptotic notion of absolute continuity of measures.