摘要
本文证明了Steinhaus和Rademacher随机幕级数所表示无限级ρ(r)的随机整函数几乎必然以每一条从原点出发的射线为没有有限Borel例外值的ρ(r)级Borel方向.
In this paper the following result has been, proved: For a random entire function of infinite order ρ(r) represented by a Rademacher or Steinhaus random power series, almost surely every ray passing through the oringin is a Borel direction of order ρ(r) and without exceptional finite values. The method introduced in this paper can be used to sim plify considerably J. E. Littlewood and A. C. Offord's proof of the analogous result for Rademacher random series in the case of finite order. (Ann. of Math. , vol. 49 (1948))
出处
《湖北大学学报（自然科学版）》
CAS
1989年第2期1-5,24,共6页
Journal of Hubei University：Natural Science
关键词
随机级数
随机整函数
BOREL方向
Random entire function of infinite order ρ(r), Borel direction of order ρ(r).
