Definition:Computably Uniformly Continuous Real Function

Definition
Let $f : \R \to \R$ be a real function.

Suppose there exists a total recursive function $d : \N \to \N$ such that:
 * For every $n \in \N$ and $x, y \in \R$ such that:
 * $\size {a - b} < \dfrac 1 {\map d n + 1}$
 * it holds that:
 * $\size {\map f a - \map f b} < \dfrac 1 {n + 1}$

Then $f$ is computably uniformly continuous.

Also known as
This property is also called effectively uniformly continuous, due to the Church-Turing Thesis.