Index
λ
system, 31
lim inf
n
A
n
, 17
lim inf
n
a
n
, 17
lim sup
n
A
n
, 17
lim sup
n
a
n
, 17
π
system, 24
π
systems and uniqueness of mea
sures, 24
π

λ
Theorem, 31
σ
algebra, 10
σ
finite, 14
algebra, 10
axiom of choice, 32
Bayes’ formula, 19
binomial distribution, 25
Borel
σ
algebra, 13
Borel
σ
algebra on
R
n
, 24
Carath´
eodory’s extension
theorem, 21
central limit theorem, 75
change of variables, 58
Chebyshev’s inequality, 66
closed set, 12
conditional probability, 18
convergence almost surely, 71
convergence in
L
p
, 71
convergence in distribution, 72
convergence in probability, 71
convexity, 66
counting measure, 15
Dirac measure, 15
distributionfunction, 40
dominated convergence, 55
equivalence relation, 31
event, 10
existence of sets, which are not Borel,
32
expectation of a random variable, 47
expected value, 47
exponential distribution on
R
, 28
extended random variable, 60
Fubini’s Theorem, 61, 62
Gaussian distribution on
R
, 28
geometric distribution, 25
H¨
older’s inequality, 67
i.i.d. sequence, 74
independence of a family of random
variables, 42
independence of a finite family of ran
dom variables, 42
independence of a sequence of events,
18