Lévy's continuity theorem

In probability theory, Lévy’s continuity theorem (or Lévy's convergence theorem), named after the French mathematician Paul Lévy, connects convergence in distribution of the sequence of random variables with pointwise convergence of their characteristic functions. This theorem is the basis for one approach to prove the central limit theorem and it is one of the major theorems concerning characteristic functions. In probability theory, Lévy’s continuity theorem (or Lévy's convergence theorem), named after the French mathematician Paul Lévy, connects convergence in distribution of the sequence of random variables with pointwise convergence of their characteristic functions. This theorem is the basis for one approach to prove the central limit theorem and it is one of the major theorems concerning characteristic functions.