Definition:Big-O Notation/Uniform
Jump to navigation
Jump to search
Definition
Let $X$ be a set.
Let $V$ be a normed vector space over $\R$ or $\C$ with norm $\norm {\, \cdot \,}$.
Let $f, g : X \to V$ be mappings.
Then $f$ is big-$\OO$ of $g$ uniformly if and only if:
- $\exists c > 0 : \forall x \in X : \norm {\map f x} \le c \cdot \norm {\map g x}$
This is denoted:
- $f = \map \OO g$