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
V
3
VI
5
VII
7
VIII
11
IX
13
X
14
XI
17
LXXIII
203
LXXIV
205
LXXV
206
LXXVI
208
LXXVII
211
LXXVIII
213
LXXIX
215
LXXX
217

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