SOME EXTENSIONS OF A LEMMA OF KOTLARSKI
SOME EXTENSIONS OF A LEMMA OF KOTLARSKI
复制标题
科特拉斯基引理的一些扩展
作者：
Kirill S. Evdokimov;H. White
本文证明了Kotlarski引理（1967，Pacific Journal of Mathematics 20（1），69-76）的条件可以大大放宽。特别是，M、U1和U2的特征函数不为零的条件可以用更弱的条件来代替：U1的特征函数可以有真实的零点，只要它的特征函数在这些点的导数不为零; U2的特征函数可以有孤立的零点数; M的特征函数不需要对它的零点有任何限制。我们还表明，Kotlarski引理成立时，尾U1是不厚于指数，无论零点的特征函数U1，U2，或M。
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, U1, and U2 are nonvanishing can be replaced with much weaker conditions: The characteristic function of U1 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 U2 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 U1 are no thicker than exponential, regardless of the zeros of the characteristic functions of U1, U2, or M.