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We herein develop a theory of contiguity in the quantum domain based upon anovel quantum analogue of the Lebesgue decomposition. The theory thusformulated is pertinent to the weak quantum local asymptotic normalityintroduced in the previous paper [Yamagata, Fujiwara, and Gill, \textit{Ann.Statist.}, \textbf{41} (2013) 2197-2217.], yielding substantial enlargement ofthe scope of quantum statistics.

Noncommutative Lebesgue decomposition and contiguity with applications in quantum statistics