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Contents
Preface
xi
Chapter 1: Motivation
§1
Why bother with measure theory?
1
§2
The cost and benefit of rigor
3
§3
Where to start: probabilities or expectations?
5
§4
The de Finetti notation
7
*§5
Fair prices
11
§6
Problems
13
§7
Notes
14
Chapter 2: A modicum of measure theory
§1
Measures and sigmafields
17
§2
Measurable functions
22
§3
Integrals
26
*§4
Construction of integrals from measures
29
§5
Limit theorems
31
§6
Negligible sets
33
*§7
L
p
spaces
36
*§8
Uniform integrability
37
§9
Image measures and distributions
39
§10
Generating classes of sets
41
*§11
Generating classes of functions
43
§12
Problems
45
§13
Notes
51
Chapter 3: Densities and derivatives
§1
Densities and absolute continuity
53
*§2
The Lebesgue decomposition
58
§3
Distances and affinities between measures
59
§4
The classical concept of absolute continuity
65
*§5
Vitali covering lemma
68
*§6
Densities as almost sure derivatives
70
§7
Problems
71
§8
Notes
75
Chapter 4: Product spaces and independence
§1
Independence
77
§2
Independence of sigmafields
80
§3
Construction of measures on a product space
83
§4
Product measures
88
*§5
Beyond sigmafiniteness
93
§6
SLLN via blocking
95
*§7
SLLN for identically distributed summands
97
*§8
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 Spring '09
 DavidPollard
 Probability

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