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Sep 9, 2011 at 19:43 comment added Valerio Capraro OK, at least in the discrete case it's the classical notion. I got a bit scared because of the "balls of fixed radius".
Sep 9, 2011 at 19:03 comment added R W In the discrete case the exponential growth rate is defined as $\limsup \frac1n \log|B_n(x)|$, where $B_n(x)$ is the ball of radius $n$ centered at a point $x$. In the continuous case instead of cardinality one takes the minimal number of balls of a fixed radius necessary to cover $B_n$.
Sep 9, 2011 at 18:50 comment added Valerio Capraro I am sorry, what do you mean by "finite exponential growth"?
Sep 9, 2011 at 18:35 history answered R W CC BY-SA 3.0