Measure Theory-Lebesguq Measure

  • Thread starter Thread starter WannaBe22
  • Start date Start date
  • Tags Tags
    Measure
WannaBe22
Messages
73
Reaction score
0

Homework Statement


Prove the set A= \bigcup_{n=1}^{\infty} ( \frac{n}{5} , \frac{n}{5} + \frac{n+1}{2^n} ) is Lebesgue measurable and calculate its measure.


Homework Equations


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 !
 
Last edited:
Physics news on Phys.org
It looks to me like
A= (\frac{1}{5}, \infty)
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Can a Pre-Measure on a Symmetric Sigma Algebra Be Extended to Borel Sets?
Replies
2
Views
1K
Infinite union of closed sets is not closed
Replies
13
Views
4K
Proof by induction for rational function
Replies
7
Views
1K
Outer Lebesgue Measure limit's proof
Replies
1
Views
1K
How to show that these sequences are summable?
Replies
1
Views
1K
Finding a closed form expression for an infinite union
Replies
2
Views
1K
Pointwise convergence for all real x
Replies
5
Views
2K
[L'Hospital's Rule] Can I Use Mathematical Induction to Prove This?
Replies
6
Views
2K
Show that the limit (1+z/n)^n=e^z holds
Replies
6
Views
2K
Limit and Integration of ##f_n (x)##
Replies
8
Views
1K

Hot Threads

Recent Insights

Back
Top