A User's Guide to Measure Theoretic Probability

Front Cover
Cambridge University Press, 2002 - Mathematics - 351 pages
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
LXXII
203
LXXIII
205
LXXIV
206
LXXV
208
LXXVI
211
LXXVII
213
LXXVIII
215
LXXIX
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
LXVII
195
LXVIII
198
LXX
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LXXI
202
LXXX
219
LXXXI
222
LXXXII
226
LXXXIII
228
LXXXIV
230
LXXXV
234
LXXXVI
237
LXXXVII
239
LXXXVIII
242
LXXXIX
244
XC
248
XCI
249
XCII
256
XCIII
258
XCIV
261
XCV
264
XCVI
266
XCVII
268
XCVIII
271
XCIX
272
C
274
CI
275
CII
276
CIII
278
CIV
280
CV
285
CVI
287
CVII
289
CX
291
CXI
292
CXII
294
CXIII
295
CXIV
296
CXV
300
CXVII
301
CXVIII
302
CXIX
303
CXX
305
CXXI
306
CXXIII
307
CXXIV
308
CXXV
310
CXXVI
312
CXXVII
313
CXXVIII
315
CXXIX
316
CXXX
317
CXXXIII
320
CXXXIV
324
CXXXV
329
CXXXVI
332
CXXXVII
334
CXXXVIII
336
CXXXIX
338
CXLI
339
CXLII
342
CXLIII
343
CXLIV
345
CXLV
347
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