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.
\ProvidesPackage{proof}[1995/05/22]
% proof.sty (Proof Figure Macros)
%
% version 2.0
% June 24, 1991
% Copyright (C) 1990,1991 Makoto Tatsuta (tatsuta@riec.tohoku.ac.jp)
%
%Modified for LaTeX-2e by L. C. Paulson
%
% This program is free software; you can redistribute it or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either versions 1, or (at your option)
% any later version.
%
% This program is distributed in the hope that it will be useful
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% Usage:
% In \documentstyle, specify an optional style `proof', say,
% \documentstyle[proof]{article}.
%
% The following macros are available:
%
% In all the following macros, all the arguments such as
% <Lowers> and <Uppers> are processed in math mode.
%
% \infer<Lower><Uppers>
% draws an inference.
%
% Use & in <Uppers> to delimit upper formulae.
% <Uppers> consists more than 0 formulae.
%
% \infer returns \hbox{ ... } or \vbox{ ... } and
% sets \@LeftOffset and \@RightOffset globally.
%
% \infer[<Label>]<Lower><Uppers>
% draws an inference labeled with <Label>.
%
% \infer*<Lower><Uppers>
% draws a many step deduction.
%
% \infer*[<Label>]<Lower><Uppers>
% draws a many step deduction labeled with <Label>.
%
% \infer=<Lower><Uppers>
% draws a double-ruled deduction.
%
% \infer=[<Label>]<Lower><Uppers>
% draws a double-ruled deduction labeled with <Label>.
%
% \deduce<Lower><Uppers>
% draws an inference without a rule.
%
% \deduce[<Proof>]<Lower><Uppers>
% draws a many step deduction with a proof name.
%
% Example:
% If you want to write
% B C
% -----
% A D
% ----------
% E
% use
% \infer{E}{
% A
% &
% \infer{D}{B & C}
% }
%
% Style Parameters
\newdimen\inferLineSkip \inferLineSkip=2pt
\newdimen\inferLabelSkip \inferLabelSkip=5pt
\def\inferTabSkip{\quad}
% Variables
\newdimen\@LeftOffset % global
\newdimen\@RightOffset % global
\newdimen\@SavedLeftOffset % safe from users
\newdimen\UpperWidth
\newdimen\LowerWidth
\newdimen\LowerHeight
\newdimen\UpperLeftOffset
\newdimen\UpperRightOffset
\newdimen\UpperCenter
\newdimen\LowerCenter
\newdimen\UpperAdjust
\newdimen\RuleAdjust
\newdimen\LowerAdjust
\newdimen\RuleWidth
\newdimen\HLabelAdjust
\newdimen\VLabelAdjust
\newdimen\WidthAdjust
\newbox\@UpperPart
\newbox\@LowerPart
\newbox\@LabelPart
\newbox\ResultBox
% Flags
\newif\if@inferRule % whether \@infer draws a rule.
\newif\if@DoubleRule % whether \@infer draws doulbe rules.
\newif\if@ReturnLeftOffset % whether \@infer returns \@LeftOffset.
\newif\if@MathSaved % whether inner math mode where \infer or
% \deduce appears.
% Special Fonts
\def\DeduceSym{\vtop{\baselineskip4\p@ \lineskiplimit\z@
\vbox{\hbox{.}\hbox{.}\hbox{.}}\hbox{.}}}
% Math Save Macros
%
% \@SaveMath is called in the very begining of toplevel macros
% which are \infer and \deduce.
% \@RestoreMath is called in the very last before toplevel macros end.
% Remark \infer and \deduce ends calling \@infer.
%TEMPORARILY DELETED BY LCP DUE TO CONFLICT WITH CLASS "amsmath.sty"
\def\@SaveMath{}
\def\@RestoreMath{}
% Macros
\def\@ifEmpty#1#2#3{\def\@tempa{\@empty}\def\@tempb{#1}\relax
\ifx \@tempa \@tempb #2\else #3\fi }
\def\infer{\@SaveMath \@ifnextchar *{\@inferSteps}{\relax
\@ifnextchar ={\@inferDoubleRule}{\@inferOneStep}}}
\def\@inferOneStep{\@inferRuletrue \@DoubleRulefalse
\@ifnextchar [{\@infer}{\@infer[\@empty]}}
\def\@inferDoubleRule={\@inferRuletrue \@DoubleRuletrue
\@ifnextchar [{\@infer}{\@infer[\@empty]}}
\def\@inferSteps*{\@ifnextchar [{\@@inferSteps}{\@@inferSteps[\@empty]}}
\def\@@inferSteps[#1]{\@deduce{#1}[\DeduceSym]}
\def\deduce{\@SaveMath \@ifnextchar [{\@deduce{\@empty}}
{\@inferRulefalse \@infer[\@empty]}}
% \@deduce<Proof Label>[<Proof>]<Lower><Uppers>
\def\@deduce#1[#2]#3#4{\@inferRulefalse
\@infer[\@empty]{#3}{\@SaveMath \@infer[{#1}]{#2}{#4}}}
% \@infer[<Label>]<Lower><Uppers>
% If \@inferRuletrue, it draws a rule and <Label> is right to
% a rule. In this case, if \@DoubleRuletrue, it draws
% double rules.
%
% Otherwise, draws no rule and <Label> is right to <Lower>.
\def\@infer[#1]#2#3{\relax
% Get parameters
\if@ReturnLeftOffset \else \@SavedLeftOffset=\@LeftOffset \fi
\setbox\@LabelPart=\hbox{$#1$}\relax
\setbox\@LowerPart=\hbox{$#2$}\relax
%
\global\@LeftOffset=0pt
\setbox\@UpperPart=\vbox{\tabskip=0pt \halign{\relax
\global\@RightOffset=0pt \@ReturnLeftOffsettrue $##$&&
\inferTabSkip
\global\@RightOffset=0pt \@ReturnLeftOffsetfalse $##$\cr
#3\cr}}\relax
% Here is a little trick.
% \@ReturnLeftOffsettrue(false) influences on \infer or
% \deduce placed in ## locally
% because of \@SaveMath and \@RestoreMath.
\UpperLeftOffset=\@LeftOffset
\UpperRightOffset=\@RightOffset
% Calculate Adjustments
\LowerWidth=\wd\@LowerPart
\LowerHeight=\ht\@LowerPart
\LowerCenter=0.5\LowerWidth
%
\UpperWidth=\wd\@UpperPart \advance\UpperWidth by -\UpperLeftOffset
\advance\UpperWidth by -\UpperRightOffset
\UpperCenter=\UpperLeftOffset
\advance\UpperCenter by 0.5\UpperWidth
%
\ifdim \UpperWidth > \LowerWidth
% \UpperCenter > \LowerCenter
\UpperAdjust=0pt
\RuleAdjust=\UpperLeftOffset
\LowerAdjust=\UpperCenter \advance\LowerAdjust by -\LowerCenter
\RuleWidth=\UpperWidth
\global\@LeftOffset=\LowerAdjust
%
\else % \UpperWidth <= \LowerWidth
\ifdim \UpperCenter > \LowerCenter
%
\UpperAdjust=0pt
\RuleAdjust=\UpperCenter \advance\RuleAdjust by -\LowerCenter
\LowerAdjust=\RuleAdjust
\RuleWidth=\LowerWidth
\global\@LeftOffset=\LowerAdjust
%
\else % \UpperWidth <= \LowerWidth
% \UpperCenter <= \LowerCenter
%
\UpperAdjust=\LowerCenter \advance\UpperAdjust by -\UpperCenter
\RuleAdjust=0pt
\LowerAdjust=0pt
\RuleWidth=\LowerWidth
\global\@LeftOffset=0pt
%
\fi\fi
% Make a box
\if@inferRule
%
\setbox\ResultBox=\vbox{
\moveright \UpperAdjust \box\@UpperPart
\nointerlineskip \kern\inferLineSkip
\if@DoubleRule
\moveright \RuleAdjust \vbox{\hrule width\RuleWidth
\kern 1pt\hrule width\RuleWidth}\relax
\else
\moveright \RuleAdjust \vbox{\hrule width\RuleWidth}\relax
\fi
\nointerlineskip \kern\inferLineSkip
\moveright \LowerAdjust \box\@LowerPart }\relax
%
\@ifEmpty{#1}{}{\relax
%
\HLabelAdjust=\wd\ResultBox \advance\HLabelAdjust by -\RuleAdjust
\advance\HLabelAdjust by -\RuleWidth
\WidthAdjust=\HLabelAdjust
\advance\WidthAdjust by -\inferLabelSkip
\advance\WidthAdjust by -\wd\@LabelPart
\ifdim \WidthAdjust < 0pt \WidthAdjust=0pt \fi
%
\VLabelAdjust=\dp\@LabelPart
\advance\VLabelAdjust by -\ht\@LabelPart
\VLabelAdjust=0.5\VLabelAdjust \advance\VLabelAdjust by \LowerHeight
\advance\VLabelAdjust by \inferLineSkip
%
\setbox\ResultBox=\hbox{\box\ResultBox
\kern -\HLabelAdjust \kern\inferLabelSkip
\raise\VLabelAdjust \box\@LabelPart \kern\WidthAdjust}\relax
%
}\relax % end @ifEmpty
%
\else % \@inferRulefalse
%
\setbox\ResultBox=\vbox{
\moveright \UpperAdjust \box\@UpperPart
\nointerlineskip \kern\inferLineSkip
\moveright \LowerAdjust \hbox{\unhbox\@LowerPart
\@ifEmpty{#1}{}{\relax
\kern\inferLabelSkip \unhbox\@LabelPart}}}\relax
\fi
%
\global\@RightOffset=\wd\ResultBox
\global\advance\@RightOffset by -\@LeftOffset
\global\advance\@RightOffset by -\LowerWidth
\if@ReturnLeftOffset \else \global\@LeftOffset=\@SavedLeftOffset \fi
%
\box\ResultBox
\@RestoreMath
}
\endinput