A User's Guide to Measure Theoretic Probability

Front Cover
Cambridge University Press, 2002 - Mathematics - 351 pages
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This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.
 

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who have not had the luxury of taking a course in measure theory.

Contents

II
1
III
3
IV
5
V
7
VI
11
VII
13
VIII
14
IX
17
LXXI
203
LXXII
205
LXXIII
206
LXXIV
208
LXXV
211
LXXVI
213
LXXVII
215
LXXVIII
217

X
22
XI
26
XII
29
XIII
31
XIV
33
XV
36
XVI
37
XVII
39
XVIII
41
XIX
43
XX
45
XXI
51
XXII
53
XXIII
58
XXIV
59
XXV
65
XXVI
68
XXVII
70
XXVIII
71
XXIX
75
XXX
77
XXXI
80
XXXII
83
XXXIII
88
XXXIV
93
XXXV
95
XXXVI
97
XXXVII
99
XXXVIII
102
XXXIX
108
XL
111
XLI
113
XLII
116
XLIII
118
XLIV
121
XLV
123
XLVI
128
XLVII
131
XLVIII
135
XLIX
138
L
142
LI
147
LII
151
LIII
152
LIV
153
LV
155
LVI
159
LVII
162
LVIII
166
LIX
169
LX
176
LXI
182
LXII
184
LXIII
186
LXIV
190
LXV
193
LXVI
195
LXVII
198
LXIX
200
LXX
202
LXXIX
219
LXXX
222
LXXXI
226
LXXXII
228
LXXXIII
230
LXXXIV
234
LXXXV
237
LXXXVI
239
LXXXVII
242
LXXXVIII
244
LXXXIX
248
XC
249
XCI
256
XCII
258
XCIII
261
XCIV
264
XCV
266
XCVI
268
XCVII
271
XCVIII
272
XCIX
274
C
275
CI
276
CII
278
CIII
280
CIV
285
CV
287
CVI
289
CVII
291
CVIII
292
CIX
294
CX
295
CXI
296
CXII
300
CXIV
301
CXV
302
CXVI
303
CXVII
305
CXVIII
306
CXX
307
CXXI
308
CXXII
310
CXXIII
312
CXXIV
313
CXXV
315
CXXVI
316
CXXVII
317
CXXVIII
320
CXXIX
324
CXXX
329
CXXXI
332
CXXXII
334
CXXXIII
336
CXXXIV
338
CXXXVI
339
CXXXVII
342
CXXXVIII
343
CXXXIX
345
CXL
347
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