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I want to find a counter example

This is the Fubini theorem for sequences:

If $$\sum^{\infty}_{n=1}\sum^{\infty}_{m=1}|a_{mn}|<\infty,$$

then

$$\sum^{\infty}_{m=1}\sum^{\infty}_{n=1}a_{mn}=\sum^{\infty}_{n=1}\sum^{\infty}_{m=1}a_{mn}.$$

Then, does there exist a sequence $\{a_{mn}\}$ such that the left and the right hand sides of equality are finite but are not equal?

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