Definition:Little-Omega Notation/Definition 3

Definition
Let $f: \N \to \R, g: \N \to \R$ be two real sequences, expressed here as real-valued functions on the set of natural numbers $\N$.

Then:
 * $\map f n \in \map \omega {\map g n}$


 * $\map g n \in \map \oo {\map f n}$
 * $\map g n \in \map \oo {\map f n}$

where $\oo$ denotes little-$\oo$ notation.

Also see

 * Equivalence of Definitions of Little-Omega Notation