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Apr 28, 2012 at 20:18 comment added Pascal Maillard @tipanverella, sorry for the late answer, I wasn't notified of your comment, strangely. The Gartner-Ellis theorem is restricted to $\mathbb R^n$, as far as I know, and here we are considering the space of empirical measures on a measurable space $S$, which can be embedded into $\mathbb R^n$ only if $S$ is finite. Maybe one can work around it by discretizing the space, though...
Apr 19, 2012 at 4:29 comment added tipanverella @Pascal Maillard, I don't think that Gartner-Ellis' theorem is restricted to finite alphabets, if that is what you are reffering to.
Apr 18, 2012 at 20:55 comment added Pascal Maillard This works whenever the $X_n$ only take a finite number of values, but can it be made rigorous in the general case?
Apr 18, 2012 at 20:01 history answered tipanverella CC BY-SA 3.0