## Positive measurable numerical function

### Set

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 | $f(x)\ge 0$ |

### Discussion

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 $u_n\uparrow f$.