The $\MarkTeX*$ Standard

Scalar, vectors, matrices and random variables:

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

General sets and special sets:

$$\begin{array}{lll} \hline \mathbf{Symbol} & \mathbf{Meaning} & \mathbf{Style} \\ \hline \set{A}, \set{B}, \set{C} & \text{General set} & \text{roman, calligraphic} \\ \varnothing & \text{Empty set} & \text{empty set symbol} \\ \mathbb{Z} & \text{Set of integers} & \text{blackboard Z} \\ \mathbb{N} & \text{Set of natural numbers} & \text{blackboard N} \\ \mathbb{R} & \text{Set of real numbers} & \text{blackboard R} \\ \mathbb{C} & \text{Set of complex numbers} & \text{blackboard C} \\ \mathrm{V}, \mathrm{W} & \text{Vector space} & \text{upright V or W} \\ \Omega & \text{Sample space} & \text{uppercase omega} \\ \mathrm{A}, \mathrm{B}, \mathrm{C} & \text{Event} & \text{roman, uppercase, upright} \\ \hline \end{array}$$

General and special functions, general and special operators:

$$\begin{array}{lll} \hline \mathbf{Symbol} & \mathbf{Meaning} & \mathbf{Style} \\ \hline f(\cdot), \mu(\cdot) & \text{General function} & \text{roman or greek, round brackets} \\ F[\cdot], \Delta[\cdot] & \text{General operator} & \text{roman or greek, square brakets} \\ \hline \end{array}$$

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 e.g. $X^{(n)}$

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.