Probability In Banach Spaces: Isoperimetry And Processes (ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge / A Series Of Modern Surveys In Mathematics)

Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed. "New isoperimetric inequalities and random process techniques have recently appeared at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (e.g. boundedness and continuity of random processes, integrability and limit theorems for vector valued random variables) and of some of their links to Geometry of Banach spaces. Its purpose is to present some of the main aspects of this theory, from the foundations to the latest developments, treated with the most recent and updated tools. In particular, the most important features are the systematic use of isoperimetry and related concentration of measure phenomena (to study integrability and limit theorems for vector valued random variables), and recent abstract random process techniques (entropy and majorizing measures). Some examples of these probabilistic ideas to classical Banach space theory complete this exposition."--pub. desc

new Isoperimetric Inequalities And Random Process Techniques Have Recently Appeared At The Basis Of The Modern Understanding Of Probability In Banach Spaces. Based On These Tools, The Book Presents A Complete Treatment Of The Main Aspects Of Probability In Banach Spaces (e.g. Boundedness And Continuity Of Random Processes, Integrability And Limit Theorems For Vector Valued Random Variables) And Of Some Of Their Links To Geometry Of Banach Spaces. Its Purpose Is To Present Some Of The Main Aspects Of This Theory, From The Foundations To The Latest Developments, Treated With The Most Recent And Updated Tools. In Particular, The Most Important Features Are The Systematic Use Of Isoperimetry And Related Concentration Of Measure Phenomena (to Study Integrability And Limit Theorems For Vector Valued Random Variables), And Recent Abstract Random Process Techniques (entropy And Majorizing Measures). Some Examples Of These Probabilistic Ideas To Classical Banach Space Theory Complete This Exposition.

Based on recent developments, such as new isoperimetric inequalities and random process techniques, this book presents a thorough treatment of the main aspects of Probability in Banach spaces, and of some of their links to Geometry of Banach spaces.