%%% R.E. Showalter/Book macros

\font\tenmsb=msbm10
\font\sevenmsb=msbm7
\font\fivemsb=msbm5
\newfam\msbfam
\textfont\msbfam=\tenmsb
\scriptfont\msbfam=\sevenmsb
\scriptscriptfont\msbfam=\fivemsb
%\edef\msbfam@{\hexnumber@\msbfam}
\def\Bbb#1{\fam\msbfam\relax#1}
\font\teneufm=eufm10
\font\seveneufm=eufm7
\font\fiveeufm=eufm5
\newfam\eufmfam
\textfont\eufmfam=\teneufm
\scriptfont\eufmfam=\seveneufm
\scriptscriptfont\eufmfam=\fiveeufm
\def\frak#1{{\fam\eufmfam\relax#1}}
\let\goth\frak

\arraycolsep 2pt

\def\thechapter{\Roman{chapter}}
\def\theequation{\thesection.\arabic{equation}}
\renewcommand{\thesection}{\arabic{section}}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{lemma}[theorem]{Lemma} 
\newcommand{\example}{\medskip\noindent {\bf Example. }}
	\def\endexample{\medskip}
\newcommand{\examples}{\medskip\noindent {\bf Examples. }}
	\def\endexamples{\medskip}
\newcommand{\definitions}{\medskip\noindent {\bf Definitions. }}
	\def\enddefinitions{\medskip}
\newcommand{\definition}{\medskip\noindent {\bf Definition. }}
	\def\enddefinition{\medskip}
\def\plainlemma#1{\medskip\par\noindent{\bf Lemma\enspace} {\it#1}\medskip\par}
\def\plaincor#1{\medskip\par\noindent{\bf Corollary\enspace}{\it#1}\medskip\par}
\def\exam#1{\medskip\par\noindent{\bf Example #1.\enspace}}
\newenvironment{proof}{\medskip\par\noindent{\it Proof\/}:\quad}{\medskip\par}
	\def\qed{\medskip}		% ends proofs, examples, definitions
\def\descriptionlabel#1{\hspace\labelsep \rm #1}
\def\exercises{\bigskip\centerline{\bf Exercises}\nobreak\smallskip}
\def\eqn#1{{\rm (\ref{eq#1})}}

\def\@listI{\leftmargin\leftmargini \parsep 1\p@ plus2\p@ minus\p@
	\topsep 1.5\p@ plus2\p@ minus4\p@
	\itemsep 1\p@ plus2\p@ minus\p@}


\newcommand{\CC}{{\Bbb C}}
\newcommand{\KK}{{\Bbb K}}
\newcommand{\RR}{{\Bbb R}}
\def\A{{\cal A}}
\def\B{{\cal B}}
\def\C{{\cal C}}
\def\D{{\cal D}}
\def\H{{\cal H}}
\def\L{{\cal L}}
\def\M{{\cal M}}
\def\P{{\cal P}}
\def\S{{\cal S}}
\def\V{{\cal V}}
\def\bu{{\bf u}}

\newcommand{\ad}{\mathop{\rm ad}\nolimits}
\newcommand{\const}{\mathop{\rm const.}\nolimits}
\newcommand{\dist}{\mathop{\rm dist}\nolimits}
\newcommand{\dom}{\mathop{\rm dom}\nolimits}
\newcommand{\ess}{\mathop{\rm ess}\nolimits}
\renewcommand{\Im}{\mathop{\rm Im}\nolimits}
\newcommand{\Ker}{\mathop{\rm Ker}\nolimits}
\newcommand{\loc}{\mathop{\rm loc}\nolimits}
\renewcommand{\Re}{\mathop{\rm Re}\nolimits}
\newcommand{\Rg}{\mathop{\rm Rg}\nolimits}
\newcommand{\supp}{\mathop{\rm supp}\nolimits}

\newcommand{\varep}{\varepsilon}
\def\hatT{\widehat T}
\def\barS{\bar S}
\def\bbarS{\skew3\bar\barS}
\def\iint{\int\!\!\int}
\def\ds{\displaystyle}
\def\tfrac#1#2{{\textstyle{#1\over#2}}}