Titlebook: Probability in Banach Spaces; Isoperimetry and Pro Michel Ledoux,Michel Talagrand Book 1991 Springer-Verlag Berlin Heidelberg 1991 Banach S

Mucosa

Gaussian Random Variablesconsidered as one of the fundamental topics of the theory since it inspires many other parts of the field both in the results themselves and in the techniques of investigation. Historically, the developments also followed this line of progress.

高贵领导

Rademacher Averagesrties we examine are entirely similar to those investigated in the Gaussian case. In this way, we will see how isoperimetric methods can be used to yield strong integrability properties of convergent Rademacher series and chaos. This is studied in Sections 4.3 and 4.4. Some comparison results are al

假设

Stable Random Variablesrandom variables. Stable random variables are fundamental in Probability Theory and, as will be seen later, also play a rôle in structure theorems of Banach spaces. The literature is rather extensive on this topic and we only concentrate here on the parts of the theory which will be of interest and

Ballad

Sums of Independent Random Variablesntation of stable random variables). On the intuitive basis of central limit theorems which approximate normalized sums of independent random variables by smooth limiting distributions (Gaussian, stable), one would expect that results similar to those presented previously should hold in a sense or i

碎石

The Strong Law of Large Numbersdent Banach space valued random variables. In this study, the isoperimetric approach of Section 6.3 demonstrates its efficiency. We only investigate extensions to vector valued random variables of some of the classical limit theorems such as the laws of large numbers of Kolmogorov and Prokhorov.

到婚嫁年龄

The Law of the Iterated Logarithm extensions both enlighten the scalar statements and describe various new interesting phenomena in the infinite dimensional setting. As in the previous chapter on the strong law of large numbers, the isoperimetric approach proves to be an efficient tool in this study. The main results described here