# Henning Kerstan

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# This website now uses MathJax

published: Sun, 17 Feb 2019, 11:21 CET – last updated: Sun, 17 Feb 2019, 11:59 CET

In order to prepare this website for math content, I’ve now implemented the JavaScript engine MathJax. Read the full article to see some examples.

# Examples

To see examples of the MathJax typesetting, here is a definition (Def. 4.2.11 of my PhD thesis) containing quite a bit of math.

## Definition 4.2.11 (The Trace Measure)

Let $(\mathcal{A}, X, \alpha)$ be a $\diamond$-PTS. For every state $x \in X$ we define the trace (sub)probability measure $\textrm{tr}(x) \colon \sigma_{\mathcal{A}^\diamond}\left(\mathcal{S}_\diamond\right) \to [0,1]$ as follows: In all four cases we require $\textrm{tr}(x)(\emptyset) = 0$. For $\diamond \in \{*, \infty\}$ we define

$\textrm{tr}(x)( \{\epsilon\} ) = \alpha(x)(\mathbb{1})$

and

$\textrm{tr}(x)\big(\{au\}\big) := \int_{x' \in X} \textrm{tr}(x')(\{u\})\textrm{dP}_a(x, x')$

for all $a \in A$ and all $u \in \mathcal{A}^*$. For $\diamond \in \{\omega, \infty\}$ we define

$\textrm{tr}(x)(\mathcal{A}^\diamond) = 1$

and

$\textrm{tr}(x)\big(au\mathcal{A}^\diamond\big) := \int_{x’ \in X} \textrm{tr}(x’)(u\mathcal{A}^\diamond)\textrm{dP}_a(x, x’)$

for all $a \in A$ and all $u \in \mathcal{A}^*$.