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Images of Gaussian random fields: Salem sets and interior points

Narn-Rueih Shieh, Yimin Xiao (2006)

Studia Mathematica

Let X = X ( t ) , t N be a Gaussian random field in d with stationary increments. For any Borel set E N , we provide sufficient conditions for the image X(E) to be a Salem set or to have interior points by studying the asymptotic properties of the Fourier transform of the occupation measure of X and the continuity of the local times of X on E, respectively. Our results extend and improve the previous theorems of Pitt [24] and Kahane [12,13] for fractional Brownian motion.

Interpolation sets for Fréchet measures

J. Caggiano (2000)

Colloquium Mathematicae

We introduce various classes of interpolation sets for Fréchet measures-the measure-theoretic analogues of bounded multilinear forms on products of C(K) spaces.

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