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syrsoN | 
Germany archoroN 
Struggling with a university math problem, I'd be interested if there was actually someone who can solve it. Let m be a measure on a set X, and let {An}_n be a sequence of subsets of X satisfying m(A1)+m(A2)+... finite Consider the set E = {x element of X : x belongs to An for infinitely many n} show that m(E) = 0.
2022-10-01 16:06
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Someone on HLTV I should add
2022-10-01 16:07
1 reply
Definition of measure: A mapping m: P(X) -> [0, +infinity] is called a measure on X if i) m(empty set) = 0 and ii) m(A) <= m(A1)+m(A2)+... whenever A is a subset {Ak} sequnce of subsets
2022-10-01 16:11
yes
2022-10-01 16:07
What math level is this bro wtf is going on
2022-10-01 16:07
3 replies
Bachelor Mathematics
2022-10-01 16:11
2 replies
😧 If m(A1)+m(A2)... Is finite doesnt that mean that each segment must = 0? Otherwise the sum would be infinite
2022-10-01 16:19
1 reply
Consider the sequence 1 + 1/2 + 1/4 + 1/8... None of the numbers are zero, but the sum of all of them is 2
2022-10-01 16:24
#5
i am | 
Hungary jadyn_x
yes
2022-10-01 16:11
I know the answer
2022-10-01 16:12
is that sum of the measures equation right? isnt the sum supposed to be zero or something also if you're being serious u should probably try math stack exchange
2022-10-01 16:12
2 replies
#9
 | 
Australia B_Tannen
+1 questions almost always get answered there. Idk what this problem is
2022-10-01 16:14
No the sum is < infinity. I don't expect anyone can actually solve it, I would just be pleasantly surprised to be proven wrong. And no I'm not serious, I'll probably get it at some point today, just need to get the right idea.
2022-10-01 16:22
i know the answer but if i tell you wont learn
2022-10-01 16:14
1 reply
+1
2022-10-01 16:24
Answer is quite obvious dont you think?
2022-10-01 16:23
1 reply
#17
 | 
Germany Teuton1813
+1 I don't get his problem
2022-10-01 16:25
Need help for middle school math lmao
2022-10-01 16:25
im so glad im done with this witchery
2022-10-01 16:26
Here's a hint. E is also called the limsup of An. You can show its equal to intersection(n=1:inf) union (k=n:inf) An. If you haven't proven that already, you should be able to show it yourself. You can use countable subadditivity and that fact that if an infinite series converges, the elements must converge to 0 to complete the proof. I'll leave the details to you, because you won't pass your class otherwise.
2022-10-01 17:32
1 reply
Oh hey that's a great idea! Using the convergence of the the union of An for all n>=m when m goes to infinity is what I missed. I was really just looking to see if there was some other mathematician in the HLTV forums, and here you are :)
2022-10-03 17:18
Basic idea: Sum{An}_n is finite means there is some sort of convergence hence there is only finitely many {An} with m{An}>1/N for all N that means x is in "Infinitely" small {An}'s keep this and it follow's m(E) has to be 0
2022-10-03 17:35
3rd Semester Maß und Integrationsthorie?
2022-10-03 17:29
2 replies
Yep, ETH Zurich
2022-10-05 15:52
Name
2022-10-05 15:54
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