On a Class of Random Variables
نویسنده
چکیده
where f(rea) =f(z) is any analytic function regular in a circle of radius R>r about the origin. We can define a particular complex valued random variable Z in the following way: \Z\ =r with probability one, and arg Z is uniformly distributed on the interval [— x, x]. We shall denote by E the linear operator which "takes the expected value" of Z and of measurable functions of Z with respect to the probability measure we have defined. Then E[Z]=0, and the first member of (1.1) is clearly E[f(Z)], so that (1.1) may be written in the form
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