29 Notations
| Notation | Description | Source |
$\sigma(\mathcal{E})$ | $\sigma$-algebra generated by $\mathcal{E}$. | Definition 21.1.6 |
| $\lambda(\mathcal{E})$ | $\lambda$-system generated by $\mathcal{E}$. | Definition 21.3.3 |
| $\sigma \otimes \tau$ | Product of ideals. | Definition 7.1.5 |
| $\text{epi}(f)$ | Epigraph of $f$. | Definition 18.1.1 |
| $\mathcal{B}_{X}$ | Borel $\sigma$-algebra on $X$. | Definition 21.2.1 |
| $\sigma(\{f_{i} \mid i \in I\})$ | $\sigma$-algebra generated by the maps $\{f_{i}\}$. | Definition 25.1.7 |
| $\bigotimes_{i \in I}\mathcal{M}_{i}$ | Product $\sigma$-algebra. | Definition 25.2.1 |
| $\mathcal{L}^{0}(X; Y)$ | Space of measurable functions from $X$ to $Y$. | Definition 25.1.2 |
| $L^{0}(X; Y)$ | Space of measurable functions from $X$ to $Y$, modulo almost everywhere equality. | Definition 25.1.2 |
| $\chi_{E} = \mathbf{1}_{E}$ | Indicator function of $E$. | Definition 25.4.1 |
| $\Sigma(X, \mathcal{M}; E)$ | Space of $E$-valued simple functions on $(X, \mathcal{M})$. | Definition 25.4.3 |
| $\Sigma^{+}(X, \mathcal{M})$ | Space of non-negative simple functions. | Definition 26.1.1 |
| $\mathcal{L}^{+}(X, \mathcal{M})$ | Space of non-negative measurable functions. | Definition 26.2.1 |
| $f_{*}\mu$ | Pushforward of $\mu$ by $f$. | Definition 22.1.8 |
| $\mu \otimes \nu$ | Product measure. | Definition 22.10.1 |
| $|\mu|$ | Total variation measure of a signed/vector measure. | Definition 23.3.2, Definition 23.3.1 |
| $\mu = \mu^{+} - \mu^{-}$ | Jordan decomposition of a signed measure. | Theorem 23.1.8 |
| $\mu \perp \nu$ | Mutual singularity. | Definition 23.5.1 |
| $\nu \ll \mu$ | $\nu$ is absolutely continuous w.r.t. $\mu$. | Definition 23.4.1 |
| $M(X, \mathcal{M}; E)$, | Space of finite $E$-valued measures. | Definition 23.7.1 |
| $\|\mu\|_{\mathrm{var}}$ | Total variation of $\mu$. | Definition 23.7.1 |
| $M_{R}(X; E)$ | Space of finite Radon $E$-valued measures on $X$. | Definition 24.3.3 |
| $\mathcal{L}^{p}(X, \mathcal{M}, \mu; E)$ | Space of $p$-integrable functions, without quotient. | Definition 15.1.1 |
| $\|f\|_{L^p}$, | $L^{p}$ norm of $f$. | Definition 15.1.2 |
| $L^{p}(X, \mathcal{M}, \mu; E)$ | Space of $p$-integrable functions, modulo equality almost everywhere. | Definition 15.1.7 |
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