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Local properties o/ sample /unctions 117 then the n-th derivative belongs to H(, C) ]or an C > O.Analyticity properties of the sample functions are discussed in the author's paper [4]. Here we mention only the following. Let (t) have a bounded spectrum, i.e., let the set E of points for which F(Z)--F(2--e) % > 0, for any e > 0, be bounded above. We shall call the least upper bound of E the boundary of the spectrum.Theorem 11. I] (t) is a stationarg Gaussian process with bounded spectrum, having as the boundar o] the spectrum the number w > 0, then almost all the sample/unctions are entire/unctions o] exponential tgpe w.

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