Add missing corollary and sections reorder

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2024-04-15 20:02:05 +02:00
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\end{description}
\end{description}
\begin{example}[Axes-aligned rectangles in $\mathbb{R}^2_{[0, 1]}$]
\section{Axes-aligned rectangles over $\mathbb{R}^2_{[0, 1]}$}
Consider the instance space $X = \mathbb{R}^2_{[0, 1]}$
and the concept class $\mathcal{C}$ of concepts represented by all the points contained within a rectangle parallel to the axes of arbitrary size.
@ -108,7 +111,7 @@
\end{remark}
\begin{theorem}[Axes-aligned rectangles in $\mathbb{R}^2_{[0, 1]}$ PAC learnability]
\begin{theorem}[Axes-aligned rectangles over $\mathbb{R}^2_{[0, 1]}$ PAC learnability]
It holds that:
\begin{itemize}
\item For every distribution $\mathcal{D}$,
@ -156,4 +159,8 @@
\textit{To be continued\dots}
\end{proof}
\end{theorem}
\end{example}
\begin{corollary}
The concept class of axis-aligned rectangles over $\mathbb{R}^2_{[0, 1]}$ is efficiently PAC learnable.
\end{corollary}