| \({\left\lVert {f} \right\rVert}_\infty \coloneqq\sup_{x\in \operatorname{dom}(f)} {\left\lvert {f(x)} \right\rvert}\) | The infinity norm, \(\sup_{x\in \operatorname{dom}(f)} {\left\lvert {f(x)} \right\rvert}\) |
| \({\left\lVert {f} \right\rVert}_{L^\infty} \coloneqq\inf\left\{{M \geq 0 {~\mathrel{\Big\vert}~}{\left\lvert {f(x)} \right\rvert} \leq M \text{ for a.e. } x }\right\}\) | The ? |
| \(f_n \overset{n \to \infty }\longrightarrow f\) | Convergence of a sequence |
| \(f(x) \overset{{\left\lvert {x} \right\rvert} \to \infty}\to 0\) | Vanishing at infinity |
| \(\displaystyle\int_{{\left\lvert {x} \right\rvert} \geq N} f \overset{N\to \infty}\longrightarrow 0\) | Having small tails |
| \(\mathcal{H}\) | A Hilbert space |
| \(X\) | Generally a topological (or metric) space |
| \({\partial}_x f = {\frac{\partial }{\partial x}\,}f = {\frac{\partial f}{\partial x}\,}\) | The partial derivative of \(f\) wrt \(x\) |