
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
July 12th, 2018, 08:58 PM  #1 
Senior Member Joined: Nov 2011 Posts: 239 Thanks: 2  Lebesgue integration  Riemann integration
What the differences between Lebesgue integration and Riemann integration?
Last edited by skipjack; July 13th, 2018 at 06:48 AM. 
July 12th, 2018, 09:41 PM  #2  
Senior Member Joined: Aug 2012 Posts: 2,082 Thanks: 595 
Here is the difference in Henri Lebesgue's own words. Quote:
Or as my professor said: In Riemann integration we chop up the xaxis into little parts. In Lebesgue integration we chop up the yaxis into little parts. Or, in Riemann integration we approximate a given function with step functions. In Lebesgue integration we approximate a given function with simple functions. Last edited by Maschke; July 12th, 2018 at 09:47 PM.  
July 13th, 2018, 04:11 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
Riemann integration requires that the region of integration be an interval or a union of intervals. Lesbesque integration only requires that the region of integration be a union of measurable sets.
Last edited by skipjack; July 13th, 2018 at 06:49 AM. 
July 13th, 2018, 10:01 AM  #4  
Senior Member Joined: Oct 2009 Posts: 611 Thanks: 188  Quote:
And we can extend Riemann integration to handle more complex domains, but that isn't used much in the single variable case, but a lot in multiple dimensions.  

Tags 
integration, lebesgue, riemann, rimman 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
A question to do with lebesgue integration  Magnitude  Real Analysis  2  September 25th, 2017 10:43 AM 
Lebesgue integration question  Fabion  Real Analysis  0  February 24th, 2014 04:39 AM 
Riemann Integration  fahad nasir  Real Analysis  2  November 29th, 2013 12:22 AM 
LEBESGUE INTEGRATION  thamy_271091  Calculus  9  December 7th, 2012 07:34 AM 
Riemann integration  watson  Real Analysis  1  December 27th, 2011 07:42 AM 