\documentclass{article} \usepackage{amssymb} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %TCIDATA{OutputFilter=LATEX.DLL} %TCIDATA{Created=Monday, June 25, 2001 17:45:57} %TCIDATA{LastRevised=Monday, March 24, 2003 13:34:17} %TCIDATA{} %TCIDATA{} %TCIDATA{CSTFile=On line bluem.cst} %TCIDATA{PageSetup=72,72,72,72,0} %TCIDATA{AllPages= %H=36 %F=36,\PARA{038
\QTR{small}{Matematick\U{e1} anal\U{fd}za II online - D\U{f4}kazy\dotfill \thepage }} %} \newtheorem{theorem}{Theorem} \newtheorem{acknowledgement}[theorem]{Acknowledgement} \newtheorem{algorithm}[theorem]{Algorithm} \newtheorem{axiom}[theorem]{Axiom} \newtheorem{case}[theorem]{Case} \newtheorem{claim}[theorem]{Claim} \newtheorem{conclusion}[theorem]{Conclusion} \newtheorem{condition}[theorem]{Condition} \newtheorem{conjecture}[theorem]{Conjecture} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{criterion}[theorem]{Criterion} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{exercise}[theorem]{Exercise} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{notation}[theorem]{Notation} \newtheorem{problem}[theorem]{Problem} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{remark}[theorem]{Remark} \newtheorem{solution}[theorem]{Solution} \newtheorem{summary}[theorem]{Summary} \newenvironment{proof}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}} \input{tcilatex} \begin{document} \author{A. U. Thor} \title{Lab Report} \date{The Date } \maketitle \begin{abstract} A Laboratory report created with Scientific Notebook \end{abstract} \section{Nutn\'{a} a posta\v{c}uj\'{u}ca podmienka integrovate\v{l}nosti} \subsection{Veta o Lebesquovej miere spo\v{c}\'{\i}tate\v{l}n\'{e}ho zjednotenia.} \textbf{D\^{o}kaz: }$\forall \varepsilon >0$ a $\forall n\in \mathbf{N}$ existuje spo\v{c}\'{\i}tate\v{l}n\'{e} zjednotenie $n$-kv\'{a}drov $\left\{ E_{k}^{\left( n\right) };\,k=1,2,\dots \right\} $ tak\'{e}, \v{z}e plat\'{\i} \[ \sum_{k=1}^{\infty }c\left( E_{k}^{\left( n\right) }\right) <\frac{% \varepsilon }{2^{n}}, \]% ktor\'{e} pokr\'{y}va $F_{n},$ t.j$.F_{n}\subseteq \bigcup_{k=1}^{n}E_{k}^{\left( n\right) }.$ Potom spo\v{c}\'{\i}tate\v{l}n% \'{y} syst\'{e}m $\left\{ E_{k}^{\left( n\right) };\,k=1,2,\dots ,\,n=1,2,\dots \right\} $ pokr\'{y}va $\bigcup_{n=1}^{\infty }F_{n}^{{}}$ a plat\'{\i} \[ \sum_{k=1}^{\infty }\sum_{n=1}^{\infty }c\left( E_{k}^{\left( n\right) }\right) =\varepsilon .\blacksquare \] \begin{center} \begin{tabular}{|c|} \hline {\small \hyperref{Sp\"{a}\v{t}}{}{}{Ma52.tex#5}} \\ \hline \end{tabular} \end{center} \rule{6.5in}{0.04in} \textsl{Matematick\'{a} anal\'{y}za II} \end{document}