High Quality Content by WIKIPEDIA articles! In mathematics — specifically, in large deviations theory — a rate function is a function used to quantify the probabilities of rare events. It is required to have several "nice" properties which assist in the formulation of the large deviation principle. In some sense, the large deviation principle is an analogue of weak convergence of probability measures, but one which takes account of how well the rare events behave.An extended real-valued function I : X ? [0, +?] defined on a Hausdorff topological space X is said to be a rate function if it is not identically +? and is lower semi-continuous, i.e. all the sub-level sets.

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