Difference between revisions of "Index of notation"
From Maths
m |
m |
||
Line 26: | Line 26: | ||
| <math>\|f\|_{L^p}=\left(\int^1_0|f(t)|^pdt\right)^\frac{1}{p}</math> - it is a [[Norm]] on <math>\mathcal{C}([0,1],\mathbb{R})</math> | | <math>\|f\|_{L^p}=\left(\int^1_0|f(t)|^pdt\right)^\frac{1}{p}</math> - it is a [[Norm]] on <math>\mathcal{C}([0,1],\mathbb{R})</math> | ||
|- | |- | ||
− | | <math> | + | | <math>\|f\|_\infty</math> |
− | | | + | | |
* Functional Analysis | * Functional Analysis | ||
* Real Analysis | * Real Analysis | ||
− | | It is | + | | It is a norm on <math>C([a,b],\mathbb{R})</math>, given by <math>\|f\|_\infty=\sup_{x\in[a,b]}(|f(x)|)</math> |
|- | |- | ||
| <math>C^k([a,b],\mathbb{R})</math> | | <math>C^k([a,b],\mathbb{R})</math> |
Revision as of 13:33, 18 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 |
⋃⋅iAi | Makes it explicit that the items in the union (the Ai) are pairwise disjoint, that is for any two their intersection is empty | |
ℓp(F) |
|
The set of all bounded sequences, that is ℓp(F)={(x1,x2,...)|xi∈F, ∞∑i=1|xi|p<∞} |
Lp |
|
Lp(μ)={u:X→R|u∈M, ∫|u|pdμ<∞}, p∈[1,∞)⊂R (X,A,μ) is a measure space. The class of all measurable functions for which |f|p is integrable |
Lp |
|
Same as Lp |
Unordered symbols
Expression | Context | Details |
---|---|---|
A/B-measurable |
|
There exists a Measurable map between the σ-algebras |