Lecture notes. Written from the material of Berkeley Stat 210A, licensed CC BY 4.0. These are notes, not a transcript: the material has been reorganised and rewritten. This adaptation carries the same licence, and the original is linked above.

22. Reader Notation Conventions¶

What this covers¶

This chapter is not a lecture but the notation key behind one: the LaTeX macro file that the STAT 210A reader loads at the start of every set of notes, so that the same shorthand renders the same way from one chapter to the next. Collecting it here means the rest of the reader can be read without re-deriving what a symbol means the first time it appears. It assumes only familiarity with basic set notation and the definition of a probability space.

Sets, spaces, and number systems¶

The reader uses calligraphic letters as generic names for sets, sigma-algebras, and spaces that get fixed once at the start of a chapter and then used silently:

$\mathcal{B}$, $\mathcal{F}$ — a sigma-algebra (e.g. of Borel sets, or of a filtration).
$\mathcal{N}$ — a family or class named in a given chapter.
$\mathcal{P}$ — a class of probability measures on the underlying space. This is the notation a theoretical-statistics course needs constantly: a statistical model is a family $\mathcal{P}$ of candidate distributions, not a single one, and a claim is often only true for every $P$ in that family rather than for one fixed $P$.
$\mathcal{X}$ — a sample space, the set an observation takes its values in.

Blackboard bold is reserved for the two standard number systems:

$\mathbb{R}$ — the real numbers.
$\mathbb{Z}$ — the integers.

Expectation and probability¶

$\mathbb{E}$ and $\mathbb{P}$ are the expectation and probability operators, also in blackboard bold, so that they read visually as "the same kind of object" as $\mathbb{R}$ and $\mathbb{Z}$ rather than as ordinary italic letters that could be confused with a variable named $E$ or $P$.

Notions of equality¶

Ordinary equality is not enough once probability is in the picture, so the reader distinguishes several weaker senses of "equal," each written as an equals sign with the qualifier stacked above it:

$\stackrel{\text{a.s.}}{=}$ — equal almost surely: equal outside a set of probability zero, under whatever probability measure is fixed by context.
$\stackrel{\mathcal{P}\text{-a.s.}}{=}$ — equal $\mathcal{P}$-almost surely: equal almost surely under every $P$ in the model class $\mathcal{P}$, not just one of them. This is the notion that matters when a statement is meant to hold uniformly over an entire statistical model.
$\stackrel{\mu\text{-a.s.}}{=}$ — equal almost everywhere with respect to a fixed measure $\mu$ that need not be a probability measure.
$\stackrel{D}{=}$ — equal in distribution: the two sides need not be equal as random variables at all, only have the same law.

Independence and identical distribution¶

$\perp\!\!\!\!\perp$ — independence, written as two crossed vertical bars rather than spelled out, since it appears inside displayed equations often enough to need its own symbol.
$\stackrel{\text{i.i.d.}}{\sim}$ — distributed independently and identically as (used for a sequence of random variables sharing one law).
$\stackrel{\text{ind.}}{\sim}$ — distributed independently as, without the identical part: each variable in the sequence may have its own law, but they remain independent.

Calculus and optimization shorthand¶

\td, rendered $\,\mathrm{d}$, inserts the small space conventionally placed before a differential, as in $\int f(x) \td x$, so integrals are typeset consistently across the reader without retyping the spacing command each time.
\argmin and \argmax typeset $\operatorname*{argmin}$ and $\operatorname*{argmax}$ as proper math operators (upright, with subscripts stacking underneath rather than to the side), the way $\sup$ or $\lim$ behave, rather than as three italic letters.
\minz and \maxz do the same for the "minimize" and "maximize" headings of an optimization display, e.g. $$\operatorname*{minimize}_{x} \ f(x) \quad \text{subject to} \quad g(x) \le 0.$$

Moments¶

$\mathrm{Var}$, $\mathrm{Cov}$, $\mathrm{Corr}$ — variance, covariance, and correlation, set in upright (non-italic) type as is conventional for a named operator rather than a product of variables.

Two versions of the macro file¶

The reader has been revised between offerings of the course. The fall-2026 version of the macro file differs from the fall-2024 version in two small ways: it fixes a copy-paste slip in which \maxz had been declared to print "minimize" (the same text as \minz) instead of "maximize," and it adds one further macro, \ep, as shorthand for $\varepsilon$. Both versions otherwise define the same set of symbols listed above.

Sources¶

statistics/berkeley/stat210a/fall-2024/reader/latex-macros.md, converted from reader/latex-macros.tex in the berkeley-stat210a/fall-2024 repository (commit 812543bde50398a54db3044bf8ba7120189a4dfa), CC BY 4.0.
statistics/berkeley/stat210a/fall-2026/reader/latex-macros.md, converted from reader/latex-macros.tex in the berkeley-stat210a/fall-2026 repository (commit 7dc8f80da94dff74532d9e3923afdb16a255262d), CC BY 4.0 — the clearer of the two (fixes the \maxz typo and adds \ep), used as the primary source for the symbol list above.

No slides, transcript, or exercises were supplied for this item; the source is the macro file itself, not a recorded lecture, so this chapter documents the notation rather than a topic.

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