Rewrite the Probability theory.
Introduced pinfreal as real numbers with infinity.
Use pinfreal as value for measures.
Introduces Lebesgue Measure based on the integral in Multivariate Analysis.
Proved Radon Nikodym for arbitrary sigma finite measure spaces.
% tutorial.sty : Isabelle Tutorial Page Layout
%
\typeout{Document Style tutorial. Released 9 July 2001}
\hyphenation{Isa-belle man-u-script man-u-scripts ap-pen-dix mut-u-al-ly}
\hyphenation{data-type data-types co-data-type co-data-types }
%usage: \iflabelundefined{LABEL}{if not defined}{if defined}
\newcommand{\iflabelundefined}[1]{\@ifundefined{r@#1}}
%%%INDEXING use isa-index to process the index
\newcommand\seealso[2]{\emph{see also} #1}
\usepackage{makeidx}
%index, putting page numbers of definitions in boldface
\def\bold#1{\textbf{#1}}
\newcommand\fnote[1]{#1n}
\newcommand\indexbold[1]{\index{#1|bold}}
% The alternative to \protect\isa in the indexing macros is
% \noexpand\noexpand \noexpand\isa
% need TWO levels of \noexpand to delay the expansion of \isa:
% the \noexpand\noexpand will leave one \noexpand, to be given to the
% (still unexpanded) \isa token. See TeX by Topic, page 122.
%%%% for indexing constants, symbols, theorems, ...
\newcommand\cdx[1]{\isa{#1}\index{#1@\protect\isa{#1} (constant)}}
\newcommand\sdx[1]{\isa{#1}\index{#1@\protect\isa{#1} (symbol)}}
\newcommand\sdxpos[2]{\isa{#1}\index{#2@\protect\isa{#1} (symbol)}}
\newcommand\tdx[1]{\isa{#1}\index{#1@\protect\isa{#1} (theorem)}}
\newcommand\tdxbold[1]{\isa{#1}\index{#1@\protect\isa{#1} (theorem)|bold}}
\newcommand\cldx[1]{\isa{#1}\index{#1@\protect\isa{#1} (class)}}
\newcommand\tydx[1]{\isa{#1}\index{#1@\protect\isa{#1} (type)}}
\newcommand\tcdx[1]{\isa{#1}\index{#1@\protect\isa{#1} (type class)}}
\newcommand\thydx[1]{\isa{#1}\index{#1@\protect\isa{#1} (theory)}}
\newcommand\attrdx[1]{\isa{#1}\index{#1@\protect\isa{#1} (attribute)}}
\newcommand\cmmdx[1]{\index{#1@\protect\isacommand{#1} (command)}}
\newcommand\commdx[1]{\isacommand{#1}\index{#1@\protect\isacommand{#1} (command)}}
\newcommand\methdx[1]{\isa{#1}\index{#1@\protect\isa{#1} (method)}}
\newcommand\tooldx[1]{\isa{#1}\index{#1@\protect\isa{#1} (tool)}}
\newcommand\settdx[1]{\isa{#1}\index{#1@\protect\isa{#1} (setting)}}
\newcommand\pgdx[1]{\pgmenu{#1}\index{#1@\protect\pgmenu{#1} (Proof General)}}
%set argument in \bf font and index in ROMAN font (for definitions in text!)
\newcommand\bfindex[1]{{\bf#1}\index{#1|bold}\@}
\newcommand\rmindex[1]{{#1}\index{#1}\@}
\newcommand\ttindex[1]{\texttt{#1}\index{#1@\texttt{#1}}\@}
\newcommand\ttindexbold[1]{\texttt{#1}\index{#1@\texttt{#1}|bold}\@}
\newcommand{\isadxpos}[2]{\isa{#1}\index{#2@\protect\isa{#1}}\@}
\newcommand{\isadxboldpos}[2]{\isa{#1}\index{#2@\protect\isa{#1}|bold}\@}
%Commented-out the original versions to see what the index looks like without them.
% In any event, they need to use \isa or \protect\isa rather than \texttt.
%%\newcommand{\indexboldpos}[2]{#1\index{#2@#1|bold}\@}
%%\newcommand{\ttindexboldpos}[2]{\texttt{#1}\index{#2@\texttt{#1}|bold}\@}
\newcommand{\indexboldpos}[2]{#1\@}
\newcommand{\ttindexboldpos}[2]{\isa{#1}\@}
%\newtheorem{theorem}{Theorem}[section]
\newtheorem{Exercise}{Exercise}[section]
\newenvironment{exercise}{\begin{Exercise}\rm}{\end{Exercise}}
\newcommand{\ttlbr}{\texttt{[|}}
\newcommand{\ttrbr}{\texttt{|]}}
\newcommand{\ttor}{\texttt{|}}
\newcommand{\ttall}{\texttt{!}}
\newcommand{\ttuniquex}{\texttt{?!}}
\newcommand{\ttEXU}{\texttt{EX!}}
\newcommand{\ttAnd}{\texttt{!!}}
\newcommand{\isasymignore}{}
\newcommand{\isasymimp}{\isasymlongrightarrow}
\newcommand{\isasymImp}{\isasymLongrightarrow}
\newcommand{\isasymFun}{\isasymRightarrow}
\newcommand{\isasymuniqex}{\isamath{\exists!\,}}
\renewcommand{\S}{Sect.\ts}
\renewenvironment{isamarkuptxt}{\begin{isamarkuptext}}{\end{isamarkuptext}}
\newif\ifremarks
\newcommand{\REMARK}[1]{\ifremarks\marginpar{\raggedright\footnotesize#1}\fi}
%names of Isabelle rules
\newcommand{\rulename}[1]{\hfill(#1)}
\newcommand{\rulenamedx}[1]{\hfill(#1\index{#1@\protect\isa{#1} (theorem)|bold})}
%%%% meta-logical connectives
\let\Forall=\bigwedge
\let\Imp=\Longrightarrow
\let\To=\Rightarrow
\newcommand{\Var}[1]{{?\!#1}}
%%% underscores as ordinary characters, not for subscripting
%% use @ or \sb for subscripting; use \at for @
%% only works in \tt font
%% must not make _ an active char; would make \ttindex fail!
\gdef\underscoreoff{\catcode`\@=8\catcode`\_=\other}
\gdef\underscoreon{\catcode`\_=8\makeatother}
\chardef\other=12
\chardef\at=`\@
% alternative underscore
\def\_{\leavevmode\kern.06em\vbox{\hrule height.2ex width.3em}\hskip0.1em}
%%%% ``WARNING'' environment: 2 ! characters separated by negative thin space
\def\warnbang{\vtop to 0pt{\vss\hbox{\Huge\bf!\!!}\vss}}
\newenvironment{warn}{\medskip\medbreak\begingroup \clubpenalty=10000
\small %%WAS\baselineskip=0.9\baselineskip
\noindent \hangindent\parindent \hangafter=-2
\hbox to0pt{\hskip-\hangindent\warnbang\hfill}\ignorespaces}%
{\par\endgroup\medbreak}
%%%% ``PROOF GENERAL'' environment
\def\pghead{\lower3pt\vbox to 0pt{\vss\hbox{\includegraphics[width=12pt]{pghead}}\vss}}
\newenvironment{pgnote}{\medskip\medbreak\begingroup \clubpenalty=10000
\small \noindent \hangindent\parindent \hangafter=-2
\hbox to0pt{\hskip-\hangindent \pghead\hfill}\ignorespaces}%
{\par\endgroup\medbreak}
\newcommand{\pgmenu}[1]{\textsf{#1}}
%%%% Standard logical symbols
\let\turn=\vdash
\let\conj=\wedge
\let\disj=\vee
\let\imp=\rightarrow
\let\bimp=\leftrightarrow
\newcommand\all[1]{\forall#1.} %quantification
\newcommand\ex[1]{\exists#1.}
\newcommand{\pair}[1]{\langle#1\rangle}
\newcommand{\lparr}{\mathopen{(\!|}}
\newcommand{\rparr}{\mathclose{|\!)}}
\newcommand{\fs}{\mathpunct{,\,}}
\newcommand{\ty}{\mathrel{::}}
\newcommand{\asn}{\mathrel{:=}}
\newcommand{\more}{\ldots}
\newcommand{\record}[1]{\lparr #1 \rparr}
\newcommand{\dtt}{\mathord.}
\newcommand\lbrakk{\mathopen{[\![}}
\newcommand\rbrakk{\mathclose{]\!]}}
\newcommand\List[1]{\lbrakk#1\rbrakk} %was \obj
\newcommand\vpile[1]{\begin{array}{c}#1\end{array}}
\newenvironment{matharray}[1]{\[\begin{array}{#1}}{\end{array}\]}
\newcommand{\Text}[1]{\mbox{#1}}
\DeclareMathSymbol{\dshsym}{\mathalpha}{letters}{"2D}
\newcommand{\dsh}{\mathit{\dshsym}}
\let\int=\cap
\let\un=\cup
\let\inter=\bigcap
\let\union=\bigcup
\def\ML{{\sc ml}}
\def\AST{{\sc ast}}
%macros to change the treatment of symbols
\def\relsemicolon{\mathcode`\;="303B} %treat ; like a relation
\def\binperiod{\mathcode`\.="213A} %treat . like a binary operator
\def\binvert{\mathcode`\|="226A} %treat | like a binary operator
%redefinition of \sloppy and \fussy to use \emergencystretch
\def\sloppy{\tolerance2000 \hfuzz.5pt \vfuzz.5pt \emergencystretch=15pt}
\def\fussy{\tolerance200 \hfuzz.1pt \vfuzz.1pt \emergencystretch=0pt}
%non-bf version of description
\def\descrlabel#1{\hspace\labelsep #1}
\def\descr{\list{}{\labelwidth\z@ \itemindent-\leftmargin\let\makelabel\descrlabel}}
\let\enddescr\endlist
% The mathcodes for the letters A, ..., Z, a, ..., z are changed to
% generate text italic rather than math italic by default. This makes
% multi-letter identifiers look better. The mathcode for character c
% is set to |"7000| (variable family) + |"400| (text italic) + |c|.
%
\DeclareSymbolFont{italics}{\encodingdefault}{\rmdefault}{m}{it}%
\def\@setmcodes#1#2#3{{\count0=#1 \count1=#3
\loop \global\mathcode\count0=\count1 \ifnum \count0<#2
\advance\count0 by1 \advance\count1 by1 \repeat}}
\@setmcodes{`A}{`Z}{"7\hexnumber@\symitalics41}
\@setmcodes{`a}{`z}{"7\hexnumber@\symitalics61}