Index of notation

Ordered symbols are notations which are (likely) to appear as they are given here, for example [math]C([a,b],\mathbb{R})[/math] denotes the continuous function on the interval [ilmath][a,b][/ilmath] that map to [ilmath]\mathbb{R} [/ilmath] - 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 [math]A[/math] comes before [math]\mathbb{A}[/math] comes before [math]\mathcal{A}[/math]

Expression	Context	Details
[math]\|\cdot\|[/math]	Functional Analysis Real Analysis	Denotes the Norm of a vector
[math]\|f\|_{C^k}[/math]	Functional Analysis	This Norm is defined by [math]\|f\|_{C^k}=\sum^k_{i=0}\sup_{t\in[0,1]}(|f^{(i)}(t)|)[/math] - note [math]f^{(i)}[/math] is the [math]i^\text{th}[/math] derivative.
[math]\|f\|_{L^p}[/math]	Functional Analysis	[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]C([a,b],\mathbb{R})[/math]	Functional Analysis Real Analysis	It is the set of all functions [math]:[a,b]\rightarrow\mathbb{R}[/math] that are continuous
[math]C^k([a,b],\mathbb{R})[/math]	Functional Analysis Real Analysis	It is the set of all functions [math]:[a,b]\rightarrow\mathbb{R}[/math] that are continuous and have continuous derivatives up to (and including) order [math]k[/math] The unit interval will be assumed when missing
[math]\ell^p(\mathbb{F})[/math]	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]
[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] [math](X,\mathcal{A},\mu)[/math] is a measure space. The class of all measurable functions for which [math]|f|^p[/math] is integrable
[math]L^p[/math]	Measure Theory	Same as [math]\mathcal{L}^p[/math]

Unordered symbols

Expression	Context	Details
[math]\mathcal{A}/\mathcal{B}[/math]-measurable	Measure Theory	There exists a Measurable map between the [ilmath]\sigma[/ilmath]-algebras