Under what circumstances does the existence of the iterated limit $\lim\limits_{x \to \infty} \left(\lim\limits_{y \to \infty}\ a_{x,y} \right)$ imply the existence of the double limit $\lim\limits_{(x,y) \to (\infty,\infty)} a_{x,y}$?
When does the existence of an iterated limit imply the existence of a double limit?
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real-analysis
limits
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0For sequences, see [this previous question](http://math.stackexchange.com/questions/15240/when-can-you-switch-the-order-of-limits). See also the Moore-Osgood Theorem. – 2011-06-03