January 20th, 2011, 09:13 AM  #1 
Member Joined: Oct 2010 Posts: 37 Thanks: 0  integrability
Show that there does not exist any function such that ,where (i). (ii). We know that boxfunctions are wellintegrable. How can the above hold then? 
January 20th, 2011, 03:41 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,443 Thanks: 564  Re: integrability
If I understand the problem correctly, the requirement is equality at every point. At the discontinuity points of f(x), ?'(x) will not be defined.

January 21st, 2011, 04:29 AM  #3  
Member Joined: Oct 2010 Posts: 37 Thanks: 0  Re: integrability Quote:
 
January 21st, 2011, 05:11 AM  #4 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: integrability but does the limit exist?

January 22nd, 2011, 06:08 AM  #5 
Member Joined: Oct 2010 Posts: 37 Thanks: 0  Re: integrability
No. In this way the problem is solved though. But it does not deal with integrability whatsoever. Whatever. Thanks. 
January 22nd, 2011, 03:09 PM  #6  
Global Moderator Joined: May 2007 Posts: 6,443 Thanks: 564  Re: integrability Quote:
 

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