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- Jan 26th 2009, 10:08 AMtransgalacticsubsequence definition question..
- Jan 26th 2009, 01:54 PMThePerfectHacker
Let .

Now,

The reason why is because is convergent.

The rest of them are similar. - Jan 28th 2009, 12:20 AMtransgalactic

this expression is not correct

X_n is bounded

the limit of the sequence doesnt equal the limsup

- Jan 28th 2009, 02:55 PMThePerfectHacker
- Jan 28th 2009, 09:22 PMtransgalactic
Xn is not convergent

its bounded - Jan 28th 2009, 09:28 PMIsomorphism
- Jan 28th 2009, 11:44 PMtransgalactic

why

X_n is a subsequence which converges

the definition of limsup

is being the sup of the limit group of every subsequence

you cant do limsup X_n

by doing that you split this subsequence into a smaller convergent subsequences

and take the Sup of their limits

which has nothing to do with limsup x_n - Jan 29th 2009, 08:27 AMThePerfectHacker