Difference between revisions of "Index of notation"
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Revision as of 01:32, 29 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=0supt∈[0,1](|f(i)(t)|) - note f(i) is the ith derivative. |
| ∥f∥Lp |
|
∥f∥Lp=(∫10|f(t)|pdt)1p - it is a Norm on C([0,1],R) |
| ∥f∥∞ |
|
It is a norm on C([a,b],R), given by ∥f∥∞=supx∈[a,b](|f(x)|) |
| Ck([a,b],R) |
|
It is the set of all functions :[a,b]→R that are continuous and have continuous derivatives up to (and including) order k The unit interval will be assumed when missing |
| \bigudot_i A_i | Makes it explicit that the items in the union (the A_i) are pairwise disjoint, that is for any two their intersection is empty | |
| \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 |
Unordered symbols
| Expression | Context | Details |
|---|---|---|
| \mathcal{A}/\mathcal{B}-measurable |
|
There exists a Measurable map between the \sigma-algebras |
| a\cdot b |
|
Vector dot product |
