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right-continuous_function [2013/09/07 22:43] nikolaj |
right-continuous_function [2014/03/21 11:11] |
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| - | ===== Right-continuous function ===== | ||
| - | ==== Definition ==== | ||
| - | | @#88DDEE: $p\in\mathbb N$ | | ||
| - | | @#FFBB00: $f\in\mathrm{RightContinous}(\mathbb R^p,\mathbb R) $ | | ||
| - | |||
| - | | @#55EE55: $f:\mathbb R^p\to\mathbb R$ | | ||
| - | |||
| - | | @#DDDDDD: $\varepsilon,\delta\in \mathbb R_+^*$ | | ||
| - | | $y\in\mathbb R^p$ | | ||
| - | |||
| - | | @#55EE55: $\forall y.\ \forall\varepsilon.\ \exists \delta.\ \forall x.\ (x\ge y\ \land\ \Vert x-y \Vert < \delta) \implies |f(x)-f(y)|<\varepsilon$ | | ||
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| - | ==== Discussion ==== | ||
| - | === Reference === | ||
| - | Wikipedia: [[http://en.wikipedia.org/wiki/Continuous_function|Continuous function]] | ||
| - | ==== Parents ==== | ||
| - | === Subset of === | ||
| - | [[Continuous function]] | ||
| - | === Context === | ||
| - | [[Real coordinate space]], [[Norm]] | ||
