Titlebook: Geometric Aspects of Probability Theory and Mathematical Statistics; V. V. Buldygin,A. B. Kharazishvili Book 2000 Springer Science+Busines

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Two classical isoperimetric problems, which are basic for further results and facts of the theory. We shall consider here two classical geometric theorems of isoperimetric type. The choice of these theorems is motivated by the circumstance that both of them are closely connected with the Brunn-Minkowski inequality.

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Book 2000, functional analysis, probability theory, the theory of differential equations and some others. Furthermore, every mathematical discipline consists of several large sections in which specific problems are investigated and the corresponding technique is developed. For example, in general topology we

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Peter K. Gessner,Teresa Gessnerr further considerations. Most theorems presented in the section will be given without proofs. For more information around this topic, we refer the reader to the fundamental monograph by Bourbaki [29] (see also [179]).

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Convex sets in vector spaces,r further considerations. Most theorems presented in the section will be given without proofs. For more information around this topic, we refer the reader to the fundamental monograph by Bourbaki [29] (see also [179]).

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Some infinite-dimensional vector spaces,n particular, on infinite-dimensional Banach spaces). Among them some widely known classical spaces consisting of sequences of real numbers can be met rather frequently. Therefore, it is reasonable to recall in this section a number of typical properties of such spaces.

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Comparison principles for Gaussian processes, preordering relations in the class Φ.(.) of real-valued positive functions given on a set . of parameters. As a rule, . will be a separable metric space. In particular, the following situations are of especial interest to us: