 Characteristic function

In mathematics, characteristic function can refer to any of several distinct concepts:
 The most common and universal usage is as a synonym for indicator function, that is the function

 which for every subset A of X, has value 1 at points of A and 0 at points of X − A.
 In probability theory, the characteristic function (probability theory) of any probability distribution on the real line is given by the following formula, where X is any random variable with the distribution in question:
 where E means expected value. This concept extends to multivariate distributions.
 The characteristic function (convex analysis) in convex analysis:
 The characteristic state function in statistical mechanics.
 The characteristic polynomial in linear algebra.
 The Euler characteristic, a topological invariant.
 The cooperative game in game theory.
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 Mathematical disambiguation
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