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I'm a little confused about the definition of limit supremum; what does it mean that the following limit is finite?

$$\limsup _{h\rightarrow \infty}\;\sup_{x\in \mathbb R}\; A(x,h)$$ where $A(x,h)$ is a function of $x$, and $h$.

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    Does it mean anything? Looks to me like you're binding $h$ twice. Did you mean something like $\displaystyle \limsup_{h \to \infty}\ \sup_{x \in \mathbb R}\ A(x,h)$?2011-08-28
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    Exactly, but I have no idea how to make it like this!2011-08-28
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    You can right-click the expression in my comment and select "Show Source" to see how I did it.2011-08-28
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    There are many different ways of defining the limit superior; one of them is the following: the limit superior is the supremum of the set of limit points.2011-08-28
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    This question seems to be related: http://math.stackexchange.com/questions/49699/about-the-notion-of-limsup-and-liminf/2011-08-28

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