Let $V$ be a paracompact strictly $K$-analytic space. Let $W\subset V$ be a compact strictly $K$-analytic domain of $V$ and let $f\colon W\to{\mathbb{R}}$ be a continuous function with $f\geq 0$. Then for any $\varepsilon>0$ there exists a piecewise ${\mathbb{Q}}$-linear function $\varphi$ on $V$ such that $\varphi\geq 0$ and for all $x\in W$ we have $f(x)-\varepsilon\leq\varphi(x)\leq f(x)$.