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real_step_function [2013/10/27 16:51] nikolaj |
real_step_function [2014/03/21 11:11] (current) |
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| ===== Real step function ===== | ===== Real step function ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $\langle X,\Sigma\rangle\in\mathrm{MeasurableSpace}(X)$ | | + | | @#55CCEE: context | @#55CCEE: $\langle X,\Sigma\rangle\in\mathrm{MeasurableSpace}(X)$ | |
| - | | @#55EE55: $f\in \mathcal T$ | | + | | @#55EE55: postulate | @#55EE55: $f\in \mathcal T$ | |
| - | | @#88DDEE: $f\in\mathrm{Measurable}(X,\mathbb R)$ | | + | | @#55CCEE: context | @#55CCEE: $f\in\mathrm{Measurable}(X,\mathbb R)$ | |
| Where we consider the Borel algebra over $\mathbb R$ | Where we consider the Borel algebra over $\mathbb R$ | ||
| - | | @#55EE55: $\mathrm{im}(f)$ ... finite | | + | | @#55EE55: postulate | @#55EE55: $\mathrm{im}(f)$ ... finite | |
| ==== Discussion ==== | ==== Discussion ==== | ||
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| === Refinement of === | === Refinement of === | ||
| [[Measurable function]] | [[Measurable function]] | ||
| - | === Requirements === | + | === Context === |
| [[Real number]] | [[Real number]] | ||
