特性関数 (確率論)
μ X ( { a < x < b } ) = 1 ( 2 π ) n lim T 1 → ∞ ⋯ lim T n → ∞ ∫ { − T ≤ t ≤ T } ∏ k = 1 n ( e − i t k a k − e − i t k b k i t k ) φ X ( t ) λ ( d t ) {\displaystyle \mu _{X}{\big (}\{a<x<b\}{\big )}={\frac {1}{(2\pi )^{n}}}\lim _{T_{1}\to \infty }\cdots \lim _{T_{n}\to \infty }\int \limits _{\{-T\leq t\leq T\}}\prod _{k=1}^{n}\left({\frac {e^{-it_{k}a_{k}}-e^{-it_{k}b_{k}}}{it_{k}}}\right)\varphi _{X}(t)\lambda (dt)} , X がベクトル型確率変数の場合