Titlebook: Gaussian Random Functions; M. A. Lifshits Book 1995 Springer Science+Business Media Dordrecht 1995 Gaussian distribution.Gaussian measure.

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Majorizing Measures,have different forms (see Theorems 14.1 and 14.5), and a certain gap may exist between these bounds. In particular, this is a reason of that it is impossible to give necessary and sufficient conditions for the boundedness (or continuity) of a Gaussian random function in terms of the entropy. In the

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Several Open Problems,., ρ), and moreover, one can construct an indicator model for this function. The converse is obviously true: If both a Brownian function . an indicator model for this function exist, then (., ρ) may be isometrically embedded into L.. However, a more natural question is the following: Does the existe

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Book 1995t all conceivable nice properties that a distribution may ever have: symmetry, stability, indecomposability, a regular tail behavior, etc. Gaussian measures (the distributions of Gaussian random functions), as infinite-dimensional analogues of tht< classical normal distribution, go to work as such e

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https://doi.org/10.1007/978-3-030-05099-3efined on an . parametric set, we shall interpret the regularity as boundedness of the sample functions, or the continuity of sample functions with respect to the intrinsic semimetric. We shall also mention some special features of the regularity of ., such as boundedness of the variation and differentiability.