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## [7860bc]: thys / Integration / document / root.tex Maximize Restore History

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 \documentclass[11pt,a4paper]{report} % further packages required for unusual symbols (see also isabellesym.sty) \usepackage{latexsym} \usepackage{amssymb} \usepackage[english]{babel} \usepackage[utf8]{inputenc} \usepackage[only,bigsqcap]{stmaryrd} \usepackage{wasysym} \usepackage{eufrak} \usepackage{textcomp} %\usepackage{apalike} %\usepackage{times} \usepackage{isabelle,isabellesym} % this should be the last package used \usepackage{pdfsetup} % proper setup for best-style documents \urlstyle{rm} \isabellestyle{it} \hyphenation{Isabelle} \renewcommand{\isamarkupheader}[1] {\markright{THEORY~\isabellecontext}} \date{15th May 2003} \parindent 0pt\parskip 0.5ex \begin{document} \title{Formalizing Integration Theory, with an Application to Probabilistic Algorithms} \author{Stefan Richter\\ LuFG Theoretische Informatik\\ RWTH Aachen\\ AhornstraĂe 55\\ 52056 Aachen\\ FRG\\ \url{richter@informatik.rwth-aachen.de}} \date{\today} \maketitle \pagestyle{headings} \tableofcontents % include generated text of all theories % \input{session} \newpage \pagestyle{headings} \input{intro} \input{Sigma_Algebra} \subsection{Monotone convergence} \label{sec:monconv} \input{MonConv} \subsection{Measure spaces} \label{sec:measure-spaces} \input{Measure} \newpage \section{Real-valued random variables} \label{sec:realrandvar} \input{RealRandVar} \chapter{Integration} \label{cha:integration} The chapter at hand assumes a central position in the present paper. The Lebesgue integral is defined and its characteristics are shown in \ref{sec:stepwise-approach}. To illustrate the problems arising in doing so, we first look at implementation alternatives that did not work out. \section{Two approaches that failed} \label{sec:two-approaches-that} \input{Failure} \section{The three-step approach} \label{sec:stepwise-approach} \input{Integral} \input{outro} \begin{flushleft} \bibliographystyle{plain} \bibliography{root} \end{flushleft} \end{document}