Formal Definition
Given a Polish space let be a sequence of Borel probability measures on, let be a sequence of positive real numbers such that, and finally let be a lower semicontinuous functional on . The sequence is said to satisfy a large deviation principle with speed and rate if, and only if, for each Borel measurable set ,
where and denote respectively the closure and interior of .
Read more about this topic: Large Deviations Theory
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