Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
positive_measurable_numerical_function [2013/08/18 20:02] nikolaj |
positive_measurable_numerical_function [2014/03/21 11:11] (current) |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| ===== Positive measurable numerical function ===== | ===== Positive measurable numerical function ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $ \langle X,\Sigma_X\rangle\in \mathrm{MeasurableSpace}(X) $ | | + | | @#55CCEE: context | @#55CCEE: $ \langle X,\Sigma_X\rangle\in \mathrm{MeasurableSpace}(X) $ | |
| - | | @#55EE55: $f\in \mathcal M^+$ | | + | | @#55EE55: postulate | @#55EE55: $f\in \mathcal M^+$ | |
| + | |||
| + | | @#55CCEE: context | @#55CCEE: $f\in \mathrm{Measurable}(X,\overline{\mathbb R})$ | | ||
| - | | @#88DDEE: $f\in \mathrm{Measurable}(X,\overline{\mathbb R})$ | | ||
| | $x\in X$ | | | $x\in X$ | | ||
| - | | @#55EE55: $f(x)\ge 0$ | | + | | @#55EE55: postulate | @#55EE55: $f(x)\ge 0$ | |
| ==== Discussion ==== | ==== 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 $u_n\uparrow f$. | 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 $u_n\uparrow f$. | ||
| - | ==== Context ==== | + | ==== Parents ==== |
| === Subset of === | === Subset of === | ||
| [[Measurable numerical function]] | [[Measurable numerical function]] | ||
