From 16555851b6514a736c5c9d8e73de7da7fc9b6288 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Thu, 20 Oct 2022 18:25:31 +0200
Subject: Migrate from 'jekyll-katex' to 'kramdown-math-sskatex'

---
 source/know/concept/renyi-entropy/index.md | 26 +++++++++++++-------------
 1 file changed, 13 insertions(+), 13 deletions(-)

(limited to 'source/know/concept/renyi-entropy')

diff --git a/source/know/concept/renyi-entropy/index.md b/source/know/concept/renyi-entropy/index.md
index d53ccc0..55f233c 100644
--- a/source/know/concept/renyi-entropy/index.md
+++ b/source/know/concept/renyi-entropy/index.md
@@ -9,7 +9,7 @@ layout: "concept"
 
 In information theory, the **Rényi entropy** is a measure
 (or family of measures) of the "suprise" or "information"
-contained in a random variable $X$.
+contained in a random variable $$X$$.
 It is defined as follows:
 
 $$\begin{aligned}
@@ -19,12 +19,12 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-Where $\alpha \ge 0$ is a free parameter.
+Where $$\alpha \ge 0$$ is a free parameter.
 The logarithm is usually base-2, but variations exist.
 
-The case $\alpha = 0$ is known as the **Hartley entropy** or **max-entropy**,
-and quantifies the "surprise" of an event from $X$,
-if $X$ is uniformly distributed:
+The case $$\alpha = 0$$ is known as the **Hartley entropy** or **max-entropy**,
+and quantifies the "surprise" of an event from $$X$$,
+if $$X$$ is uniformly distributed:
 
 $$\begin{aligned}
     \boxed{
@@ -33,9 +33,9 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-Where $N$ is the cardinality of $X$; the number of different possible events.
-The most famous case, however, is $\alpha = 1$.
-Since $H_\alpha$ is problematic for $\alpha \to 1$, we must take the limit:
+Where $$N$$ is the cardinality of $$X$$; the number of different possible events.
+The most famous case, however, is $$\alpha = 1$$.
+Since $$H_\alpha$$ is problematic for $$\alpha \to 1$$, we must take the limit:
 
 $$\begin{aligned}
     H_1(X)
@@ -44,7 +44,7 @@ $$\begin{aligned}
 \end{aligned}$$
 
 We then apply L'Hôpital's rule to evaluate this limit,
-and use the fact that all $p_i$ sum to $1$:
+and use the fact that all $$p_i$$ sum to $$1$$:
 
 $$\begin{aligned}
     H_1(X)
@@ -64,9 +64,9 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-Next, for $\alpha = 2$, we get the **collision entropy**, which describes
+Next, for $$\alpha = 2$$, we get the **collision entropy**, which describes
 the surprise of two independent and identically distributed variables
-$X$ and $Y$ yielding the same event:
+$$X$$ and $$Y$$ yielding the same event:
 
 $$\begin{aligned}
     \boxed{
@@ -76,9 +76,9 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-Finally, in the limit $\alpha \to \infty$,
+Finally, in the limit $$\alpha \to \infty$$,
 the largest probability dominates the sum,
-leading to the definition of the **min-entropy** $H_\infty$,
+leading to the definition of the **min-entropy** $$H_\infty$$,
 describing the surprise of the most likely event:
 
 $$\begin{aligned}
-- 
cgit v1.3