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Positive measurable numerical function
Definition
| $ \langle X,\Sigma_X\rangle\in \mathrm{MeasurableSpace}(X) $ |
| $f\in \mathcal M^+$ |
| $f\in \mathrm{Measurable}(X,\overline{\mathbb R})$ |
| $x\in X$ |
| $f(x)\ge 0$ |
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 $u_n\uparrow f$.
Parents
Subset of
