Characteristic function

In mathematics, characteristic function can refer to any of several distinct concepts:

\mathbf{1}_A: X \to \{0, 1\}
which for every subset A of X, has value 1 at points of A and 0 at points of X − A.
\varphi_X(t) = \operatorname{E}\left(e^{itX}\right)\,
where E means expected value. This concept extends to multivariate distributions.
\chi_{A} (x)�:= \begin{cases} 0, & x \in A; \\ %2B \infty, & x \not \in A. \end{cases}