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(, F, )
G F
f L1(, F, )
g L1(, G, )
A
f d=
A
g d
A G E[f | G] g
f
G
0 G 0 (, G)
0(A) =(A) A G (, G)
(A) =A
f d0 A G 0
g L1(, G, )
A
g d0= (A)
A G
A
g d =
A
g d0= (A) =
A
f d0=
A
f d
E[f | G]
G
A
f d=A
E[f | G]d
A G
E[f | G] E[f | G]
E[f | G] f
L1(, F, )
G = {, } E[f | G] =
f d := E[f] E[f]
G
A
E[f] d= A
f d
A=
A=
G=F E[f | G] =f f G
P F
G=(P)
E[f | G]() =h() :=
CP
1C() 1
(C)
C
f d
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h G A G
(P) ={ CQC : Q P}
A= CQ
C Q P
A
h d=
CQ
C
h d=
CQ
C
( 1
(C)
C
f d) d=
CQ
C
f d=
A
f d
G F E[ | G]
L1(, F, ) L1(, G, )
E[ | G]
E[ | G]
g L(, G, ) E[g f | G] =g E[f | G] fL1(, F, )
B G fL1(, F, )
E[E[f | G]| B] =E[E[f | B]| G] =E[f | B]
f, g L1(, F, ) , R E[f | G] + E[g | G]
G
A G
A
E[f | G] + E[g| G] d= A
E[f | G] d + A
E[g| G] d=
=
A
f d +
A
g d=
A
f+ g d
E[f+ g | G] =E[f | G] + E[g| G]
fL1(, F, ) E[ | G] E[f | G]L1
fL1 A = {E[f | G] 0} E[f | G] G
A, Ac G
E[f | G]L1 =
A
E[f | G] d +
Ac
E[f | G] d=
=
A
f d +
Ac
f d
A
|f| d +
Ac
|f| d= fL1
f L1(, F, ) A G 1A E[f | G] G
B G
B
1A E[f | G] d=
AB
E[f | G] d=
AB
f d=
B
1A f d=
B
E[1A f | G] d
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E[ | G]
g L(, G, )
g 0
{sj}j=1
L(, G, ) 0 s1 s2
... g sjj
g B G
B
g E[f | G] d= limj
B
sj E[f | G] d= limj
B
sj f d=
B
g f d
E[g f | G] = g E[f | G] g g = g+ g
E[f | B]
G
E[E[f | B]| G] =E[f | B]
E[E[f | G]| B] =E[f | B] B B
B
E[f | G] d=
B
f d=
B
E[f | B] d
E[f | B] B E[E[f | G]| B] =E[f | B]
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