| context | $ \langle X,\Sigma_X\rangle\in \mathrm{MeasurableSpace}(X) $ |
| postulate | $f\in \mathcal M^+$ |
| context | $f\in \mathrm{Measurable}(X,\overline{\mathbb R})$ |
| $x\in X$ |
| postulate | $f(x)\ge 0$ |
For the definition of the integral, it's crucial to know that for every $f\in \mathcal M^+$, there is a sequence $u_n$ with elements in the step functions $\mathcal T^+$, with $u_n\uparrow f$.