Make font size smaller in remark systematically

Question

My LaTeX begins with \documentclass[9pt,a4paper,reqno]{amsbook}. I want the font size of "Remark" even smaller, is there a way to do this systematically? (But the other parts keep unchanged.)

And maybe better with different font (most part it looks like Times New Roman, and in Theorem environment it's italian, I want the font in "Remark" to be more different).

My "Remark" is defined like this:

\theoremstyle{plain}
\newtheorem{thm}{Theorem}[section]
\newtheorem{remark}[thm]{Remark}

Thanks in advance!

Answer 1

The trick is to initiate \small before the remark, which needs to ensure the previous paragraphs has ended.

\documentclass{article}
\usepackage{amsthm}

\usepackage{lipsum}

\theoremstyle{plain}
\newtheorem{thm}{Theorem}[section]

\theoremstyle{definition}
\newtheorem{zremark}[thm]{Remark}

\newenvironment{remark}{\par\small\zremark}{\endzremark}

\begin{document}

\lipsum*[3]

\begin{thm}
\lipsum[1][1-2]
\end{thm}

\lipsum[2][1-3]

\begin{remark}
\lipsum[3][1]
\end{remark}

\lipsum[4]

\end{document}

If you want to change the font family in remarks, the simplest way is to define a new theorem style.

\documentclass{article}
\usepackage{amsthm}

\usepackage{lipsum}

\newtheoremstyle{myremark}% name of the style to be used
  {\topsep}% measure of space to leave above the theorem. E.g.: 3pt
  {\topsep}% measure of space to leave below the theorem. E.g.: 3pt
  {\sffamily\upshape}% name of font to use in the body of the theorem
  {0pt}% measure of space to indent
  {\sffamily\bfseries}% name of head font
  {.}% punctuation between head and body
  { }% space after theorem head; " " = normal interword space
  {}% standard setting


\theoremstyle{plain}
\newtheorem{thm}{Theorem}[section]

\theoremstyle{myremark}
\newtheorem{remark}[thm]{Remark}

\begin{document}

\lipsum*[3]

\begin{thm}
\lipsum[1][1-2]
\end{thm}

\lipsum[2][1-3]

\begin{remark}
\lipsum[3][1]
\end{remark}

\lipsum[4]

\end{document}