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Interchanging limits

Author Message
Guest
Posted: Wed Mar 21, 2007 9:50 pm
Hi all,

I think I knew this once but I've forgotten a lot of math...

what conditions on the sequence a_{m,n} do we need to justify an
interchange of limits and obtain

\lim_{m \rightarrow \infty} \lim_{n \rightarrow \infty} a_{m,n} =
\lim_{n \rightarrow \infty} \lim_{m \rightarrow \infty} a_{m,n}

?

Thanks in advance for your help, people!

Best,
LH
 
Nik
Posted: Thu Mar 22, 2007 2:20 am
Guest
On 22 อมา, 08:50, lhi...@gmail.com wrote:
[quote:3c36806de1]Hi all,

I think I knew this once but I've forgotten a lot of math...

what conditions on the sequence a_{m,n} do we need to justify an
interchange of limits and obtain

\lim_{m \rightarrow \infty} \lim_{n \rightarrow \infty} a_{m,n} =
\lim_{n \rightarrow \infty} \lim_{m \rightarrow \infty} a_{m,n}

?

Thanks in advance for your help, people!

Best,
LH
[/quote:3c36806de1]
a_{t,n} is uniform convergence for t.
 
 
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