Is there a standard definition for a lacunary sequence?
Suppose $0 < a_1 < a_2 < \cdots.$
I've read two papers using the term recently. One requires $$ \lim_n\frac{a_{n+1}}{a_n}>1 liminf_n\frac{a_{n+1}}{a_n}>1 $$ while the other only requires $$ \lim_na_{n+1}-a_n=+\infty. $$
The two differ, of course: $a_1=1,\ a_{n+1}=a_n+\sqrt{a_n}$ has a ratio that tends to 1 but a difference that diverges.
Further, the EOM entry for lacunary sequence is different from both (a finite form of the first): $$ \frac{a_{n+1}}{a_n}\ge\lambda>1. $$
