Formatting misunderstanding\

Question

I have the following latex script:

\newtheorem*{BellOpV}{Definition}
\begin{BellOpV}
$V^{\pi}$ is defined as $T^{\pi}:\mathbb{R}^{|S|} \to \mathbb{R}^{|S|}$. It maps value functions to value functions.

$$(T^{\pi}V^{\pi})(s) = \sum_{a \in A} \pi(a|s) \left[ R(s,a) + \gamma \sum_{s' \in S} P(s' | s,a) V^{\pi}(s') \right]$$
\end{BellOpV}

The \emph{Bellman Operator for $V^{\pi}$} defined before has the following properties:

\begin{enumerate}
\item[]{$V^{\pi}$ is a \emph{fixed point} for $V^{\pi}$ that means that $T^{\pi}V^{\pi} = V^{\pi}$}
\item[]{$T^{\pi}$ is linear}
\item[]{if $0<\gamma<1$ then $T^{\pi}$ is a \emph{maximum-norm contraction}}
\end{enumerate}

The output of my code is the following:

My question is why from "The Bellman Operator ..." is all shifted on the right? Seems it is part of the definition, which is unwanted. How can I fix this?

Answer 1

Your code may be improved in several ways, listed here in no particular order:

• Don't use $$ to initiate and terminate displaymath mode in a LaTeX document. Instead, use \[ and \]. See the posting Why is \[ ... \] preferable to $$ ... $$? for an in-depth discussion of this matter.

• Use \colon instead of : in definition.

• Use an itemize environment instead of an enumerate environment, and terminate each sentence with a period (dot, full stop); after all, they are full English-language sentences.

• Use \mid instead of | to denote the conditioning events.

• Typographically speaking, the square brackets generated by \left[ and \right] are too big. Use \biggl[ and \biggr] instead.

• Finally, if you absolutely, positively must suppress the paragraph indentation for the paragraph that follows the defintion, simply prefix it with a \noindent directive.

\documentclass{article}
\usepackage{amsthm,  % for '\newtheorem*' macro
            amssymb} % for '\mathbb' macro
\newtheorem*{BellOpV}{Definition}
\begin{document}

\begin{BellOpV}
$V^{\pi}$ is defined as $T^{\pi}\colon\mathbb{R}^{|S|} \to \mathbb{R}^{|S|}$. It maps value functions to value functions.
\[
(T^{\pi}V^{\pi})(s) = \sum_{a\in A} \pi(\,a\mid s\,) 
\biggl[ R(s,a) + \gamma \sum_{s'\in S} P(\,s'\mid s,a\,) V^{\pi}(s') \biggr]
\]
\end{BellOpV}

\noindent  % <--- are you sure you really want this?
The \emph{Bellman Operator} for $V^{\pi}$ defined before has the following properties:
\begin{itemize}
\item $V^{\pi}$ is a \emph{fixed point} for $V^{\pi}$, i.e.,  $T^{\pi}V^{\pi} = V^{\pi}$.
\item $T^{\pi}$ is linear.
\item If $0<\gamma<1$ then $T^{\pi}$ is a \emph{maximum-norm contraction}.
\end{itemize}

\end{document}

Answer 2

The phrase “Bellman Operator” is part of the definition! It must appear in it, but earlier.

\documentclass{article}
\usepackage{amsmath,amssymb,amsthm}

\theoremstyle{definition}
\newtheorem*{definition}{Definition}

\begin{document}

\begin{definition}
The \emph{Bellman Operator for $V^{\pi}$} is defined as 
$T^{\pi}\colon\mathbb{R}^{|S|} \to \mathbb{R}^{|S|}$ by
\[
(T^{\pi}V^{\pi})(s) = 
\sum_{a \in A} \pi(a|s) \Bigl[ 
  R(s,a) + \gamma \sum_{s' \in S} P(s' \mid s,a) V^{\pi}(s')
\Bigr]
\]
It maps value functions to value functions.
\end{definition}

The Bellman operator for $V^{\pi}$ defined above has the following properties:
\begin{itemize}
\item $V^{\pi}$ is a \emph{fixed point} for $V^{\pi}$, which means 
      that $T^{\pi}V^{\pi} = V^{\pi}$;
\item $T^{\pi}$ is linear;
\item if $0<\gamma<1$ then $T^{\pi}$ is a \emph{maximum-norm contraction}.
\end{itemize}

\end{document}

You may not want the line \theoremstyle{definition} before defining the definition environment; in this case the text will be italicized, except for the argument of \emph which would be in upright type. Usually definitions are typeset in upright type and only the defined term is in italics.

Points to note:

1. Never leave a blank line before a display

2. Think twice before leaving a blank line after a display, which means starting a new paragraph

3. Never use $$

4. The clause “It maps…” should go after the definition

5. The text about the properties is a new paragraph, so it should be indented

6. There's absolutely no need to use \newtheorem in front of every such environment

7. The enumerate or itemize environment should not have a blank line in front of it, because it's introduced by a clause

8. It's “which means”, not “that means”

Here's the rendering.

If you feel that \mid leaves too wide a space around the |, at least use \,|\, (and better define a macro).

By the way, I can't make sense of such a definition; please, check the part $V^{\pi}$ is a \emph{fixed point} for $V^{\pi}$, because it doesn't seem to mean anything sensible.

Answer 3

This is paragraph indentation. Just remove the blank line between \end{BellOpV} and The \emph{Bellman Operator for $V^{\pi}$}....

Comment aside: never use $$ ... $$ with LaTeX. This is plain TeX syntax and yields bad spacing. Use \[ ... \] instead.

Answer 4

I solved in the following way:

\newtheorem{BellOpV}{Definition}
\AfterEndEnvironment{BellOpV}{\noindent\ignorespaces}