Index
Symbols
&(Q), Bore l sigma-algebr a o n Q 2 4
Bin(n , p), binomia l distributio n 8
C(X) , continuou s function s fro m X t o R 4 9
C , th e comple x number s x v
Cb(X), bounde d continuou s function s fro m
X t o R 9 4
CcpQ, compactl y supporte d continuou s func -
tions fro m X t o R 9 4
C£°(R
fc
), infinitel y differentiat e function s
of compac t suppor t fro m R
fc
t o R 111
Cov(X , V), covarianc e betwee n X an d Y 6 7
EX , expectatio n o f X 3 9
E[X; A] = E[X1
A
] = f
A
XdP 3 9
Geom(p), geometri c distributio n 8
L p , rando m variable s wit h p finit e absolut e
moments 3 9
ifP, completio n o f LP 4 3
N(fj,, cr
2),
norma l distributio n 11
N , th e natura l number s x v
^ ( n ) , th e powe r se t o f Cl 2 4
Poiss(A), Poisso n distributio n 9
Q, th e rational s x v
R, th e rea l number s x v
S
n _ 1
, th e uni t spher e i n R
n
102
SD(X), standar d deviatio n o f X 6 7
Unif(a, 6) , unifor m distributio n 11
VarX, varianc e o f X 6 7
X + , th e positiv e element s o f X x v
Z, th e integer s x v
a.e., almos t everywher e 4 3
a.s., almos t surel y 4 3
dv/dfj,, Radon—Nikody m derivativ e 4 7
/ + = max( / ,0 ) 3 8
/ - = m a x ( - / ,0 ) 3 8
i.i.d., independen t identicall y distribute d 6 8
m c ( ^ ) , monoton e clas s generate d b y srf 3 0
imiLP(M) = (/i/i
p
w
1 /p
3 9
||X||p = (EIIXIP])
1
/** 3 9
i / ^ , absolut e continuit y 4 7
r(X), c r ( ^ ) , . .. sigma-algebr a generate d b y
X , ^ , et c 24 , 49 , 120
A, V, th e mi n an d ma x operator s xv i
A
Absolute continuit y . . 11, see also Measur e
Adams, Willia m J 2 2
Adapted proces s 126, 182
Aldous, Davi d J 157
Almost everywher e convergenc e 4 3
Almost sur e
central limi t theore m 9 0
convergence 4 3
Alon, Nog a 8 9
Andre, Desir e 179, 180
Approximation t o th e identit y 20 5
Avogadro, Lorenz o Roman o Amede o Carl o
159
Azuma, Kazuok i 157
Azuma-Hoeffding inequalit y . . 155, see also
Heoffding's inequalit y
B
Bachelier, Loui s Jean Baptist e Alphons e 159,
177, 180
Backward [o r reversed ] martingal e 155
Banach, Stefa n 157
Bass, Richar d Frankli n 20 1
Baxter, Marti n 157
Berkes, Istva n 9 0
217
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