SOME EXTENSIONS OF A LEMMA OF KOTLARSKI
放宽了Kotlarski引理的条件，允许U1的特征函数有实零点（只要导数非零）、U2有孤立零点、M无限制，且U1尾部不超过指数分布时引理仍成立。
This note demonstrates that the conditions of Kotlarski’s (1967, Pacific Journal of Mathematics 20(1), 69–76) lemma can be substantially relaxed. In particular, the condition that the characteristic functions of M , U 1 , and U 2 are nonvanishing can be replaced with much weaker conditions: The characteristic function of U 1 can be allowed to have real zeros, as long as the derivative of its characteristic function at those points is not also zero; that of U 2 can have an isolated number of zeros; and that of M need satisfy no restrictions on its zeros. We also show that Kotlarski’s lemma holds when the tails of U 1 are no thicker than exponential, regardless of the zeros of the characteristic functions of U 1 , U 2 , or M .