Notes:Measures - Real and Abstract Analysis - Hewitt & Stromberg

From Maths
Jump to: navigation, search

Overview

A continuation of the Notes:Measures series, covering the terminology used in Books:Real and Abstract Analysis - Edwin Hewitt & Karl Stromberg.

Definitions

(Carathéodory) Outer Measure

For a set [ilmath]X[/ilmath], a function, [ilmath]\mu[/ilmath] defined on [ilmath]\mathcal{P}(X)[/ilmath] (the power-set of [ilmath]X[/ilmath]) is a Carathéodory Outer Measure if:

  1. [ilmath]0\le \mu(A)\le +\infty[/ilmath] [ilmath]\forall A\in\mathcal{P}(X)[/ilmath]