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Existence of Infinite Product Measures

Juan Carlos Sampedro

Abstract

A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This result generalises the ones given up to date.

Existence of Infinite Product Measures

Abstract

A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This result generalises the ones given up to date.

Paper Structure

This paper contains 3 sections, 10 theorems, 47 equations.

Table of Contents

  1. Introduction
  2. A Key Result
  3. Construction of the Measure

Key Result

Theorem 1.1

Given $\{(\Omega_{i},\Sigma_{i},\mu_{i})\}_{i\in\mathbb{N}}$ a family of probability spaces, there exists a unique probability measure $\bigotimes_{i\in\mathbb{N}}\mu_{i}$ on the measurable space $(\bigtimes_{i\in\mathbb{N}}\Omega_{i},\bigotimes_{i\in\mathbb{N}}\Sigma_{i})$ satisfying E2 for every $

Theorems & Definitions (16)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Theorem 2.1
  • Lemma 2.2
  • proof
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • proof
  • ...and 6 more