单p-函数的识别

Recognition of Simple p-functions

本文证明了,若标准p—函数p(t)满足下列条件1)0<q=(?)(1-p(t))/t<∞;2)(?)[p(t)]^(1/t)=1;3)((lim)/(t→∞))~[μ((t,∞))]^(1/t)=0,其中μ是p(t)的典则测度;则p(t)是单p—函数.

In this paper,we have proved that,if standard p-function p satisfies follow-ing conditions:1)0<q=(?)(1-p(t))/(t)<∞,2)(?)[p(t)]^(1/t)=1,3)(?)[μ((t,∞))]^(1/t)=0, where μ is the canonical measure of p,then p is a simple p-funrtion.