Measure Theory-Lebesguq Measure


by WannaBe22
Tags: measure, theorylebesguq
WannaBe22
WannaBe22 is offline
#1
Dec9-10, 05:06 AM
P: 76
1. The problem statement, all variables and given/known data
Prove the set [tex] A= \bigcup_{n=1}^{\infty} ( \frac{n}{5} , \frac{n}{5} + \frac{n+1}{2^n} ) [/tex] is Lebesgue measurable and calculate its measure.


2. Relevant equations
3. The attempt at a solution
I've proved the set is measurable...But how can I calculate its measure?


I will be delighted to get some guidance

Thanks in advance !
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HallsofIvy
HallsofIvy is offline
#2
Dec9-10, 07:27 AM
Math
Emeritus
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Thanks
PF Gold
P: 38,882
It looks to me like
[tex]A= (\frac{1}{5}, \infty)[/tex]


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