随机函数的亏值

THE DEFICIENT VALUE OF RANDOM FUNCTION

假设f(z)为单位圆内的亚纯函数,且满足(?)T(r,f)=∞,Q(z)为非常数有理函数,X(ω)为连续型随机变量,则有结论:随机函数g_ω(z)=f(z)+X(ω)Q(z)几乎必然没有有限亏值。若f(z)为复平面上的亚纯函数,我们也有类似的结论。

Suppose that f(z) is a meromorphic function in the unit circle and (?)T(r, f)=∝, that Q(z) is a rational function and not constant, that x(ω)is a bounded random variable of continued type,then the random function, y_ω(z)=f(z)+X(ω)Q(z) has not almost surely finite deficient value.If f(z) is a meromorphic function in the plane, we have a analogous result too.