\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand*\HyPL@Entry[1]{}
\HyPL@Entry{0<</S/D>>}
\citation{Ram}
\citation{Nat}
\citation{Wil}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{2}{section.1}}
\newlabel{thm:1}{{1}{2}{}{theorem.1}{}}
\newlabel{eq:sum1overn}{{1}{2}{Introduction}{equation.1.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2}A lemma}{3}{section.2}}
\newlabel{lem:1}{{2}{3}{}{theorem.2}{}}
\newlabel{eq:xtominus1/2}{{2}{3}{}{equation.2.2}{}}
\newlabel{eq:logxovern}{{3}{3}{}{equation.2.3}{}}
\newlabel{eq:Ckj}{{4}{3}{}{equation.2.4}{}}
\newlabel{eq:errorlog}{{5}{3}{}{equation.2.5}{}}
\newlabel{eq:logxovern2}{{6}{3}{}{equation.2.6}{}}
\newlabel{eq:Bj}{{7}{4}{A lemma}{}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}The proof of Theorem\nobreakspace  {}\ref  {thm:1}}{5}{section.3}}
\newlabel{eq:j-1}{{7}{5}{The proof of Theorem~\ref {thm:1}}{equation.3.7}{}}
\newlabel{eq:E}{{8}{6}{The proof of Theorem~\ref {thm:1}}{equation.3.8}{}}
\newlabel{eq:F}{{9}{6}{The proof of Theorem~\ref {thm:1}}{equation.3.9}{}}
\newlabel{eq:G}{{10}{6}{The proof of Theorem~\ref {thm:1}}{equation.3.10}{}}
\newlabel{eq:j}{{11}{7}{The proof of Theorem~\ref {thm:1}}{equation.3.11}{}}
\bibcite{Nat}{1}
\bibcite{Ram}{2}
\bibcite{Wil}{3}
\@writefile{toc}{\contentsline {section}{\numberline {4}Acknowledgments}{8}{section.4}}
