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right-continuous_function [2013/09/07 22:42] nikolaj created |
right-continuous_function [2014/03/21 11:11] (current) |
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===== Right-continuous function ===== | ===== Right-continuous function ===== | ||
- | ==== Definition ==== | + | ==== Set ==== |
- | | @#88DDEE: $p\in\mathbb N$ | | + | | @#55CCEE: context | @#55CCEE: $p\in\mathbb N$ | |
- | | @#FFBB00: $f\in\mathrm{RightContinous}(\mathbb R^p,\mathbb R) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $f\in\mathrm{RightContinuous}(\mathbb R^p,\mathbb R) $ | |
- | | @#55EE55: $f:\mathbb R^p\to\mathbb R$ | | + | | @#55EE55: postulate | @#55EE55: $f:\mathbb R^p\to\mathbb R$ | |
- | | @#DDDDDD: $\varepsilon,\delta\in \mathbb R_+^*$ | | + | | @#DDDDDD: range | @#DDDDDD: $\varepsilon,\delta\in \mathbb R_+^*$ | |
| $y\in\mathbb R^p$ | | | $y\in\mathbb R^p$ | | ||
- | | @#55EE55: $\forall\varepsilon.\ \exists \delta.\ \forall x.\ (x\ge y\ \land\ \Vert x-y \Vert < \delta) \implies |f(x)-f(y)|<\varepsilon$ | | + | | @#55EE55: postulate | @#55EE55: $\forall y.\ \forall\varepsilon.\ \exists \delta.\ \forall x.\ (x\ge y\ \land\ \Vert x-y \Vert < \delta) \implies |f(x)-f(y)|<\varepsilon$ | |
==== Discussion ==== | ==== Discussion ==== | ||
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=== Subset of === | === Subset of === | ||
[[Continuous function]] | [[Continuous function]] | ||
- | === Context === | + | === Related === |
[[Real coordinate space]], [[Norm]] | [[Real coordinate space]], [[Norm]] |