
2^{li} £ 1. 
E  [  L(C_{n},X_{1}^{n})  ]  ³ H_{n}(P) 
L( 

^{n}) ³ logP  ( 

^{n}). 
P  {  L(X_{1}^{n}) £ logP(X_{1}^{n})a_{n}  }  £ 2^{an}. 




= 



P(x_{1}^{n}) 
é ê ê ë 
L_{i} + log 

P(x_{1}^{n}) 
ù ú ú û 
. 
log 
æ ç ç è 


P(x_{1}^{n}) 
ö ÷ ÷ ø 
£ R_{n}^{*}(S) £ log 
æ ç ç è 


P(x_{1}^{n}) 
ö ÷ ÷ ø 
+1. 
R_{n}^{*}(P  )= 

R^{*}(C_{n}, P). 

(P  ) = 

E_{x1n}  [  R_{n}(C_{n}, P; x_{1}^{n})  ]  , 
0 £  <  logp_{1}  >  £  <  logp_{2}  >  £ ... £  <  logp_{An}  >  £ 1 (where  <  x  >  = x  ë x û) 

p_{i} 2 

+ 

p_{i} 2 

£ 1. 
Q^{*}(x_{1}^{n})= 

. 
R_{n}^{*}(S) = R_{n}^{*}(Q^{*}) + log 
æ ç ç è 


P(x_{1}^{n}) 
ö ÷ ÷ ø 
, 
R_{n}^{*}(Q^{*}) = 1  <  logq_{j0}  > 
R_{n}^{*}(P_{p}) =  

+ o(1) = 0.5287 + o(1). 

^{H} (P  ) = 


P(x_{1}^{n}) R_{n}(C_{n}, P; x_{1}^{n}). 

= R_{n}^{*}+Q(1)=log 
æ ç ç è 


P(x_{1}^{n}) 
ö ÷ ÷ ø 
+ Q(1). 

= 


= 


= 

 2 ln2 + o(1) » 0.113705639. 
This document was translated from L^{A}T_{E}X by H^{E}V^{E}A.