On the Li--Zheng theorem
On the Li--Zheng theorem
By the well-known I.Kotlarski lemma, if $\xi_1$, $\xi_2$, and $\xi_3$ are independent real-valued random variables with nonvanishing characteristic functions, $L_1=\xi_1-\xi_3$ and $L_2=\xi_2-\xi_3$, then the distribution of the random vector $(L_1, L_2)$ determines the distributions of the random variables $\xi_j$ up to shift. Siran Li and Xunjie Zheng generalized this result …