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:
“This is no argument against teaching manners to the young. On the contrary, it is a fine old tradition that ought to be resurrected from its current mothballs and put to work...In fact, children are much more comfortable when they know the guide rules for handling the social amenities. It’s no more fun for a child to be introduced to a strange adult and have no idea what to say or do than it is for a grownup to go to a formal dinner and have no idea what fork to use.”
—Leontine Young (20th century)
“The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.”
—Ralph Waldo Emerson (1803–1882)