Lower semicomputable function

A function $f:X\to \mathbf{R}$ is lower semicomputable iff there exists a computable function $g:X\times \mathbf{N}\to \mathbf{Q}$ such that:

• for all $x\in X$ and all natural numbers $n$, we have $g(x,n+1)\ge g(x,n)$
• for all $x\in X$ we have $\underset{n\to \mathrm{\infty }}{lim}g(x,n)=f(x)$