# LaTeX2HTML 96.1 (Feb 5, 1996)
# Associate images original text with physical files.
$key = q/{_inline}${tildeZ_i}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$underlineg${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Prleft{lim_Ntoinftysup_thetainThetaBig|1overNsum_i=1^Ng(x_i,theta)Big|=0right}=1.eqno(12){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}overlinelim_NtoinftyPleft{sup_|theta-theta'|ledelta|H_N(theta)-H_N(theta')|;SPMgt;epsilonright};SPMlt;epsilon.eqno(15){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$|theta-theta'|ledelta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$|G_N|longrightarrow0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}1overNsum_i=1^Ninf_theta'inB(theta,epsilon)g(x_i,theta')le1overNsum_i=1^Ng(x_i,theta')le1overNsum_i=1^Nsup_theta'inB(theta,epsilon)g(x_i,theta').eqno(8){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$H_N(theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Prleft{limsup_Ntoinftysup_thetainThetaBig|1overNsum_i=1^Ng(x_i,theta)Big|leetaright}=1.eqno(11){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}sup_thetainThetaBig|1overNsum_i=1^Ng(x_i,theta)Big|to0quadmboxwithprobability1.eqno(4){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta;SPMgt;0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}|tildeZ_i|equivsup_thetainThetaleft|g(tildex_i,theta)right|.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${tildeX_1,ldots,tildeX_N}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}limsup_Ntoinftysup_theta'inB(theta,epsilon)Big|1overNsum_i=1^Ng(x_i,theta')Big|lemaxbigg[Big|E{underlineg(tildex,theta,epsilon)}Big|,Big|E{overlineg(tildex,theta,epsilon)}Big|bigg].eqno(10){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${B(theta_1,epsilon),ldots,B(theta_K,epsilon)}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}1overNsum_i=1^NtildeZ_ilongrightarrowmboxboldmath$0$quadmboxwithprobability1,{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeZ_i=g(tildex_i,cdot)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$fincalF${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$h(x,theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sup_N|H_N(theta)|;SPMlt;+infty${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeZ_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$G_N(theta)equiv1Nsum_i=1^Ng(x_i,theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Theta=[0,1]${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}left|1overNsum_i=1^NtildeZ_iright|longrightarrow0,{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mboxboldmath$0$${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$eta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$delta;SPMgt;0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${eta_j}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{|h(tildex,theta)|}=int|h(x,theta)|F(dx);SPMlt;+infty${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$inf${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$|g(x,theta)|;SPMlt;d(x)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildex_iinX${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${B(theta,epsilon)}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}sup_theta'inB(theta,epsilon)Big|1overNsum_i=1^Ng(x_i,theta')Big|lemaxleft[Big|1overNsum_i=1^Ninf_theta'inB(theta,epsilon)g(x_i,theta')Big|,Big|1overNsum_i=1^Nsup_theta'inB(theta,epsilon)g(x_i,theta')Big|right].eqno(9){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$eta;SPMgt;0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon;SPMgt;0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${G_N}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{d(tildex)};SPMlt;infty${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$g(tildex_i,theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$H:ThetatoR${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}|H_N-H|equivsup_thetainTheta|H_N(theta)-H(theta)|longrightarrow0quadmboxwithprobability1.eqno(2){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{g(tildex,theta)}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}g_N(theta)=left{arrayllNtheta;SPMamp;0lethetale1overN(2-Ntheta);SPMamp;1overN;SPMlt;thetale2overN0;SPMamp;mboxotherwisearrayright.eqno(13){displaymath}/;
$cached_env_img{$key} = '';
$key = q/{_inline}$g(x,theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$|Z|${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$B(theta,epsilon)={theta'Big|,|theta'-theta|;SPMlt;epsilon}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$G_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$H_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$calF${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}H_N(theta)equiv1overNsum_i=1^Nh(tildex_i,theta)longrightarrowE{h(tildex,theta)}equivH(theta).eqno(1){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${x_i}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$G_N(theta)equiv{sup_mgeNH_m(theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$overlineg(x,theta,epsilon)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}lim_epsilonto0overlineg(x,theta,epsilon)=g(x,theta).eqno(6){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}overlineg(x,theta,epsilon)equivsup_{theta'Big|,|theta'-theta|;SPMlt;epsilon}g(x,theta').eqno(5){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$thetainTheta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{|tildeZ_i|};SPMlt;+infty${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$xinX${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildeZ_i}=mboxboldmath$0$${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${tildex_i}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${tildeZ_1,ldots,tildeZ_N}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${g_N}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilonto0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${H_N}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$H(theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$ZinB${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$g_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Theta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sup${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}|f(theta)-f(theta')|;SPMlt;epsilon.eqno(14){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$|g_N|=1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta'${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${g(tildex_i,theta)}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}g(x,theta)=h(x,theta)-E{h(tildex,theta)}eqno(3){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}lim_epsilonto0E{overlineg(tildex,theta,epsilon)}=E{g(tildex,theta)}=0.eqno(7){displaymath}/;
$cached_env_img{$key} = '';
$key = q/{_inline}$overlineg${_inline}/;
$cached_env_img{$key} = ' 
';
1;