Theory of Random Sets

Front Cover
Springer Science & Business Media, May 11, 2005 - Mathematics - 488 pages

Stochastic geometry is a relatively new branch of mathematics. Although its predecessors such as geometric probability date back to the 18th century, the formal concept of a random set was developed in the beginning of the 1970s. Theory of Random Sets presents a state of the art treatment of the modern theory, but it does not neglect to recall and build on the foundations laid by Matheron and others, including the vast advances in stochastic geometry, probability theory, set-valued analysis, and statistical inference of the 1990s.

The book is entirely self-contained, systematic and exhaustive, with the full proofs that are necessary to gain insight. It shows the various interdisciplinary relationships of random set theory within other parts of mathematics, and at the same time, fixes terminology and notation that are often varying in the current literature to establish it as a natural part of modern probability theory, and to provide a platform for future development.

 

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Contents

I
1
II
4
III
13
IV
18
V
20
VI
22
VII
25
VIII
31
LXIV
209
LXV
213
LXVI
218
LXVII
220
LXVIII
221
LXIX
223
LXX
224
LXXI
226

IX
37
X
40
XI
41
XII
42
XIII
43
XIV
46
XV
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XVI
49
XVII
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XVIII
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XIX
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XX
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XXI
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XXII
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XXIII
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XXIV
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XXV
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XXVI
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XXVII
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XXVIII
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XXIX
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XXX
90
XXXI
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XXXII
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XXXIII
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XXXIV
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XXXV
105
XXXVI
112
XXXVII
115
XXXVIII
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XXXIX
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XL
124
XLI
127
XLII
129
XLIII
132
XLIV
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XLV
145
XLVI
150
XLVII
160
XLVIII
161
XLIX
165
L
170
LI
174
LII
176
LIII
178
LIV
182
LV
183
LVI
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LVII
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LVIII
190
LIX
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LX
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LXI
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LXII
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LXIII
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LXXIII
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LXXIV
232
LXXV
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LXXVI
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LXXVII
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LXXVIII
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LXXIX
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LXXX
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LXXXI
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LXXXII
247
LXXXIII
253
LXXXIV
258
LXXXV
262
LXXXVI
265
LXXXVII
269
LXXXVIII
270
LXXXIX
272
XC
275
XCI
277
XCII
278
XCIII
281
XCIV
284
XCV
286
XCVI
288
XCVII
293
XCVIII
295
XCIX
299
C
303
CI
312
CII
319
CIII
322
CIV
325
CV
329
CVI
334
CVII
336
CVIII
348
CIX
353
CX
361
CXI
363
CXII
366
CXIII
369
CXIV
378
CXV
387
CXVI
398
CXVII
402
CXVIII
409
CXIX
412
CXX
421
CXXI
425
CXXII
428
CXXIII
435
CXXIV
463
CXXV
467
CXXVI
475
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Page 436 - Aumann, RJ, and Shapley, LS (1974), Values of Non-Atomic Games, Princeton University Press, Princeton, NJ.

About the author (2005)

Ilya Molchanov is Professor of Probability Theory in the Department of Mathematical Statistics and Actuarial Science at the University of Berne, Switzerland.