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
V
3
VI
5
VII
7
VIII
11
IX
13
X
14
XI
17
LXXXI
203
LXXXII
205
LXXXIII
206
LXXXIV
208
LXXXV
211
LXXXVIII
213
LXXXIX
215
XC
217

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