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Chapter 1 Probability Theory in Banach Spaces: An Introductory Survey

Identifiers
DOI: 10.1016/s0076-5392(08)60804-8
Disciplines
  • Mathematics

Abstract

Publisher Summary The chapter presents a survey of those basic concepts and theorems of probability theory in Banach spaces required for the formulation and study of random equations in Banach spaces. The chapter introduces the notion of a Banach space-valued random variable and presents an introductory survey of probability theory in Banach spaces. The chapter discusses random variables defined on (Ω, Ԅ, μ) with values in (ԛ, ԅ), where ԛ is a Banach space and ԅ is the σ-algebra of Borel subsets of ԛ. he theory presented in this chapter yields the results of classical probability theory. The chapter presents some basic definitions and concepts from the theory of Banach spaces. The chapter introduces the notion of a Banach space-valued random variable, and presents a rather complete survey of the basic definitions, concepts, and theorems. The chapter discusses Banach space-valued random functions; and studies probability measures on Banach spaces. The chapter discusses some limit theorems for Banach space-valued random variables. This chapter presents an introductory survey of results from the theory of probability in Banach spaces, which are useful in the development of a theory of random equations.

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