The $\MarkTeX*$ Standard

Some rules to follow

WORK IN PROGRESS

This is an opinionated standard.

1. Test

Scalar, vectors, matrices and random variables:

$$\begin{array}{l|ll} \hline \mathbf{Symbol} & \mathbf{Meaning} & \mathbf{Style} \\ \hline a, b, c, \alpha, \beta, \gamma & \text{Scalar} & \text{roman or greek, lowercase, italic} \\ \dvec{x}, \dvec{y}, \dvec{z}, \gvec{\alpha}, \gvec{\beta}, \gvec{\gamma} & \text{Vector} & \text{roman or greek, lowercase, bold + upright if roman} \\ \dmat{A}, \dmat{B}, \dmat{C}, \dmat{\Gamma}, \dmat{\Sigma}, \dmat{\Phi} & \text{Matrix} & \text{roman or greek, uppercase, bold, upright} \\ X, Y, Z & \text{Random variable} & \text{roman, uppercase, italic} \\ \rvec{X}, \rvec{Y}, \rvec{Z} & \text{Random vector} & \text{roman, uppercase, bold, italic} \\ \hline \end{array}$$

General sets and special sets:

$$\begin{array}{l|ll} \hline \mathbf{Symbol} & \mathbf{Meaning} & \mathbf{Style} \\ \hline \setA, \setB, \setC & \text{Set} & \text{roman, calligraphic} \\ \varnothing & \text{Empty set} & \text{empty set symbol} \\ \mathbb{Z} & \text{Set of integers} & \text{blackboard Z} \\ \mathbb{N} & \text{Set of natural numbers} & \text{blackboard N} \\ \mathbb{R} & \text{Set of real numbers} & \text{blackboard R} \\ \mathbb{C} & \text{Set of complex numbers} & \text{blackboard C} \\ \Omega & \text{Sample space} & \text{uppercase omega} \\ \mathrm{A}, \mathrm{B}, \mathrm{C} & \text{Event} & \text{roman, uppercase, upright} \\ \hline \end{array}$$

General and special functions, general and special operators:

\begin{array}{l|ll} \hline \mathbf{Symbol} & \mathbf{Meaning} & \mathbf{Style} \\ \hline f\of{\cdot}, \mu\of{\cdot} & \text{Function} & \text{roman or greek, round brackets} \\ F\of{\cdot}, \Delta\if{\cdot} & \text{Operator} & \text{roman or greek, square brackets} \\ \hline \end{array}

TODO

to support reading flow - avoid display math wherever possible - avoid using parentheses in text (not math-mode) wherever possible, wrap text in commas instead - avoid itemize and enumitem, use them only if their use strictly increases and improves reading flow - only a tot number (how many?) of envs per subsection, not too many or else reading flow will suffer - plural in definition and proposition names (e.g. Counting measures) and singular in examples (e.g. Counting measure) - if they exist, official lemma and proposition names should be used (e.g. Weierstrass)

- the idea is not to introduce yet another tool for interactive content, for that jupyter notebooks and such exist, but rather to have a uniform way of dealing with publications on the web - therefore COMMANDS THAT ARE NOT REPLICABLE THROUGH TEX ARE NOT ALLOWED IN MARKTEX - Use capitalization for propositions and theorems, e.g. Novikov's Condition, Itô's Lemma, Girsanov's Theorem - superscript only if in parentheses to avoid confusion e.g. $X^{(n)}$ - if a block has only math no need for dot at the end - functions should normally be lowercase - we use

\hat

for estimators and

\check

for estimates - use notes only in two cases: - to append important complementary information to a block - to define global usage of expression (e.g. “Unless stated otherwise, we will write “random variable” for real random variables.”)

$\floor{x}$

$\ceil{x}$

$\sup\of{x,y}$

$\sup(x,y)$

$\exp{a}$

$f(x,y), f(x,y), f(x,y), f(x,y)$

$f\of{x,y}, f\of{x,y}, f\of{x,y}, f\of{x,y}$

$\dv{x}{y}$

$\pdn{n}{x}{y}$

A statement $S$ is either true or false but not both. Let $S_1$ and $S_2$ be two statements. We write “$S_1 \implies S_2$” if $S_1$ implies $S_2$. We write “$S_1 \iff S_2$”, “$S_1$ if and only if $S_2$” or “$S_1$ iff $S_2$” if $S_1 \implies S_2$ and $S_2 \implies S_1$. Further, the symbol “$:$” denotes such that, $\forall$ means for all and $\exists$ means there exists.

- rule for events (always use \ev*, e.g. \evA, if part of a sigma algebra!) - use a binding for two part adjectives (e.g. non-negative, right-continuous instead of nonnegative or right continuous)