July 25th, 2013, 03:37 AM  #1 
Senior Member Joined: Feb 2013 Posts: 153 Thanks: 0  Measure
1. What is Lebesgue measure of set N? (I found somewhere it's infinity, but, i think it's zero...) 2. If i have infinite sum of countable many functions (sum of some sequence), can I write this as countable many infinite sums sums of that function? For example, SUM(a1+a2+....)=SUM(a1)+SUM(a2)+... (where sum is infinite, for example from 0 to infinity). 
July 25th, 2013, 12:36 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 717  Re: Measure Quote:
2) If the sum is absolutely convergent, yes. Otherwise  maybe.  
July 26th, 2013, 04:12 AM  #3 
Senior Member Joined: Feb 2013 Posts: 153 Thanks: 0  Re: Measure
For the first question. So, measure of countable set is 0. If measure is 0, is that set countabe? Is that If and only if?

July 26th, 2013, 12:28 PM  #4  
Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 717  Re: Measure Quote:
 
July 26th, 2013, 12:47 PM  #5  
Senior Member Joined: Aug 2012 Posts: 2,357 Thanks: 740  Re: Measure Quote:
https://en.wikipedia.org/wiki/Cantor_set  

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