My Math Forum  

Go Back   My Math Forum > College Math Forum > Real Analysis

Real Analysis Real Analysis Math Forum

LinkBack Thread Tools Display Modes
November 15th, 2015, 07:02 AM   #1
Joined: Nov 2015
From: oman

Posts: 5
Thanks: 0

help in real analysis

What is the difference between measure and outer measure ?

Last edited by greg1313; November 15th, 2015 at 08:45 PM.
saifns is offline  
November 15th, 2015, 09:12 PM   #2
Global Moderator
Joined: May 2007

Posts: 6,660
Thanks: 648

You need to fully understand the meaning of measurable sets. All sets have outer measure, but only measurable sets have measure.
mathman is offline  
November 18th, 2015, 07:00 AM   #3
Joined: Nov 2015
From: Pennsylvania USA

Posts: 12
Thanks: 0

It's confusing because measure, outer measure, and inner measure all use the same algorithm. We can apply that same algorithm to any set.

When we have a "nice" set, then outer measure and inner measure agree, and we say the set is measurable, and we drop "outer" and "inner" and simply speak of the set's measure.

But if we have an "not nice" (i.e., non-measurable set) then inner and outer measure don't agree so the measure of the set is undefined.
ADAdamo is offline  

  My Math Forum > College Math Forum > Real Analysis

analysis, real

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
real analysis anjuzz New Users 1 July 11th, 2014 10:56 PM
Real analysis sasindu Real Analysis 4 May 9th, 2014 11:38 AM
Prove between Real Analysis and Complex Analysis uniquesailor Real Analysis 2 January 3rd, 2012 10:56 PM
real analysis elenaas Real Analysis 2 October 4th, 2009 02:36 PM
real analysis rose3 Real Analysis 2 September 1st, 2009 10:35 AM

Copyright © 2019 My Math Forum. All rights reserved.