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 $u \in \mathcal{A}^*$.