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Both sides previous revision Previous revision Next revision | Previous revision | ||
real_step_function [2013/08/16 19:45] 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: $f\in\mathrm{MeasurableFunction}(X,\mathbb R)$ | | + | | @#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: $\mathrm{im}(f)$...[[glossary|finite]] | | + | | @#55EE55: postulate | @#55EE55: $\mathrm{im}(f)$ ... finite | |
==== Discussion ==== | ==== Discussion ==== | ||
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with $\alpha_j$'s real numbers and $E_n$'s in the measurable algebra. | with $\alpha_j$'s real numbers and $E_n$'s in the measurable algebra. | ||
- | ==== Context ==== | + | ==== Parents ==== |
=== Refinement of === | === Refinement of === | ||
[[Measurable function]] | [[Measurable function]] | ||
- | === Requirements === | + | === Context === |
[[Real number]] | [[Real number]] |