Difference between revisions of "Index of notation"
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*Functional Analysis | *Functional Analysis | ||
| The set of all bounded sequences, that is <math>\ell^p(\mathbb{F})=\{(x_1,x_2,...)|x_i\in\mathbb{F},\ \sum^\infty_{i=1}|x_i|^p<\infty\}</math> | | The set of all bounded sequences, that is <math>\ell^p(\mathbb{F})=\{(x_1,x_2,...)|x_i\in\mathbb{F},\ \sum^\infty_{i=1}|x_i|^p<\infty\}</math> | ||
| + | |- | ||
| + | | <math>\mathcal{L}^p</math> | ||
| + | | | ||
| + | * Measure Theory | ||
| + | | <math>\mathcal{L}^p(\mu)=\{u:X\rightarrow\mathbb{R}|u\in\mathcal{M},\ \int|u|^pd\mu<\infty\},\ p\in[1,\infty)\subset\mathbb{R}</math><br/> | ||
| + | <math>(X,\mathcal{A},\mu)</math> is a [[Measure space|measure space]]. The class of all [[Measurable function|measurable functions]] for which <math>|f|^p</math> is integrable | ||
| + | |- | ||
| + | | <math>L^p</math> | ||
| + | | | ||
| + | * Measure Theory | ||
| + | | Same as <math>\mathcal{L}^p</math> | ||
|} | |} | ||
Revision as of 10:51, 12 March 2015
Ordered symbols are notations which are (likely) to appear as they are given here, for example C([a,b],R) denotes the continuous function on the interval [a,b] that map to R - this is unlikely to be given any other way because "C" is for continuous.
Ordered symbols
These are ordered by symbols, and then by LaTeX names secondly, for example A comes before A comes before A
| Expression | Context | Details |
|---|---|---|
| ∥⋅∥ |
|
Denotes the Norm of a vector |
| ∥f∥Ck |
|
This Norm is defined by ∥f∥Ck=k∑i=0sup - note f^{(i)} is the i^\text{th} derivative. |
| \|f\|_{L^p} |
|
\|f\|_{L^p}=\left(\int^1_0|f(t)|^pdt\right)^\frac{1}{p} - it is a Norm on \mathcal{C}([0,1],\mathbb{R}) |
| C([a,b],\mathbb{R}) |
|
It is the set of all functions :[a,b]\rightarrow\mathbb{R} that are continuous |
| C^k([a,b],\mathbb{R}) |
|
It is the set of all functions :[a,b]\rightarrow\mathbb{R} that are continuous and have continuous derivatives up to (and including) order k The unit interval will be assumed when missing |
| \ell^p(\mathbb{F}) |
|
The set of all bounded sequences, that is \ell^p(\mathbb{F})=\{(x_1,x_2,...)|x_i\in\mathbb{F},\ \sum^\infty_{i=1}|x_i|^p<\infty\} |
| \mathcal{L}^p |
|
\mathcal{L}^p(\mu)=\{u:X\rightarrow\mathbb{R}|u\in\mathcal{M},\ \int|u|^pd\mu<\infty\},\ p\in[1,\infty)\subset\mathbb{R} (X,\mathcal{A},\mu) is a measure space. The class of all measurable functions for which |f|^p is integrable |
| L^p |
|
Same as \mathcal{L}^p |
