
Real Analysis Real Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 9th, 2009, 03:04 PM  #1 
Newbie Joined: Feb 2009 Posts: 2 Thanks: 0  Give an example of a sequence of integrable functions that..
Can you guys think of any exampleS? Give an example of a sequence of integrable functions {fn} (going from 1 to infinity) on [0,1] that converges pointwise to a non integrable function f:[0,1]>R 
February 9th, 2009, 05:15 PM  #2 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: Give an example of a sequence of integrable functions that..
Riemann or Lebesgue integrable? If it's Riemann, consider defined by Then, but as converges pointwise to the function which is not Riemann integrable (but is Lebesgue integrable). If you want a series of functions that converge pointwise to a nonLebesgueintegrable function, then it's too late for my brain to work sufficiently... 
February 9th, 2009, 05:32 PM  #3 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: Give an example of a sequence of integrable functions that..
OK, maybe it's not too late... consider given by Then and converges pointwise to the function which is not integrable on [0,1]. 

Tags 
functions, give, integrable, sequence 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
integrable functions  kapital  Calculus  10  July 26th, 2012 08:36 AM 
Differentiability of Riemann Integrable Functions  veronicak5678  Real Analysis  1  April 15th, 2012 02:12 PM 
On Continuous, Integrable Functions on [0,1]  guynamedluis  Real Analysis  8  September 30th, 2011 09:37 AM 
Two likes give a negative, two unlikes give positive  WHY?  sharp  Elementary Math  3  October 27th, 2010 03:36 PM 
sequence of analytic functions  eskimo343  Complex Analysis  0  January 27th, 2010 06:42 PM 