My Math Forum measure of unbounded set

 October 13th, 2013, 01:09 PM #1 Newbie   Joined: Oct 2013 Posts: 25 Thanks: 0 measure of unbounded set Suppose A is not a bounded set and m(A?B)?(3/4)m(B) for every B. what is m(A)?? here, m is Lebesgue Outer Measure My attemption is : Let An=A?[-n,n], then m(A)=lim m(An)= lim m(An?[-n,n]) ? lim (3/4)m([-n,n]) = infinite. is my solution right? I am confusing m(A) < infinite , it doest make sence for me. Could someone help me???
October 14th, 2013, 02:30 AM   #2
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Re: measure of unbounded set

Quote:
 m(A?B)?(3/4)m(B) for every B
choosing B = A, you get m(A) <=.75m(A), that is m(A)=0.

Quote:
 I am confusing m(A) < infinite , it doest make sence for me.
You didn't show that m(A)<inf, you did show that m(A)<=inf.

October 14th, 2013, 02:34 AM   #3
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Re: measure of unbounded set

Quote:
Originally Posted by csak
Quote:
 m(A?B)?(3/4)m(B) for every B
choosing B = A, you get m(A) <=.75m(A), that is m(A)=0.

[quote:1ulqxtmx] I am confusing m(A) < infinite , it doest make sence for me.
You didn't show that m(A)<inf, you did show that m(A)<=inf.[/quote:1ulqxtmx]

Thanks , i get the point. !!

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