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Jan 20, 2011 at 20:27 comment added Anthony Quas A nice simple argument. I think though that as long as the $t_i$ are incommensurable and you assume some regularity of the $N(t)$ (such as being monotonic) I think you do get more strict versions of asymptotic.
Jan 20, 2011 at 20:13 history answered Did CC BY-SA 2.5