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Questions about characteristic functions, of a set (which gives $1$ if the element is on the set and $0$ otherwise) or of a random variable (its Fourier transform). Do not use this tag if you are asking about the method of characteristics in PDE or the characteristic polynomial in linear algebra.

Given a set $A \subseteq X$, the characteristic function of $A$ is the function $\chi_A : X \to \mathbb{R}$ given by

$$\chi_A(x) = \begin{cases} 1 & x \in A\\\ 0 & x \notin A. \end{cases}$$

Characteristic function defined as above is a synonym for indicator function.

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