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
Famous quotes containing the words formal and/or definition:
“The bed is now as public as the dinner table and governed by the same rules of formal confrontation.”
—Angela Carter (1940–1992)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)