Lévy's continuity theorem states that if characteristic <functions> $\phi_n$ converge pointwise to a <function> $\phi$ continuous at zero, then $\phi$ is a characteristic <function> and the corresponding laws converge weakly to its law. Conversely, convergence in distribution implies <pointwise convergence> of characteristic <functions>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 1 / 27H / a / Solution

 Solution (source code)