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Loeve M. — Probability Theory (part 1)
Loeve M. — Probability Theory (part 1)

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Название: Probability Theory (part 1)

Автор: Loeve M.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: fourth edition

Год издания: 1977

Количество страниц: 425

Добавлена в каталог: 19.05.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$c_r$-inequality      157
$L_{r^-}$, completeness theorem      163
$L_{r^-}$, convergence theorem      164
$L_{r^-}$, spaces      162
$\mu^0$-measurable      88
$\sigma$-additive      83 111
$\sigma$-field(s)      59
$\sigma$-field(s), compound      156 235
$\sigma$-field(s), independent      236
$\sigma$-field(s), induced      64
$\sigma$-field(s), product      61 62
$\sigma$-field(s), tail      241
Abel theorem      400
Addition Property      10
Additive set function      83
Additive set function, $\sigma$-additive      83 111
Additive set function, $\sigma$-finite      83 111
Additive set function, continuity      85
Additive set function, continuity theorem      85
Additive set function, countably      83
Additive set function, decomposition      87
Additive set function, decomposition theorem      88
Additive set function, extension      88
Additive set function, extension theorem      88
Additive set function, finite      83 111
Additive set function, finitely      83
Additive set function, restriction      88
Adherence      66
Adherent point      66
Alexandrov      190 409
Allard      44
Almost everywhere      112
Almost everywhere, convergence      114
Almost everywhere, mutual convergence      114
Almost sure(ly)      148
Almost sure(ly), convergence      152 248 260
Almost sure(ly), mutual convergence      153
Almost sure(ly), stability      244 249 274 260
Almost sure(ly), stability criterion      264
Almost uniform convergence      140
Andersen      368 379 404 411
Andersen and Jessen      92 408
Andersen, equivalence      377 391
Andersen, equivalence lemma      378
Andre, Desire      47
Arcsine law      379 404
Asymptotic behaviour theorem      399
Asymptotic passage theorem      36
Asymptotic uniform negligibility      302
atom      100
Attraction, domain of      360
Attraction, partial      403
Attraction, stability and—criteria      364
Attraction, standard      402
Axioms of the countable case      16
Axioms of the finite case      8
Baire, category theorem      75
Baire, functions      109
Banach      407
Banach, space      81
Base of a cylinder      62
Base, countable      72
Bawly      302 410
Baxter      369 390 411
bernoulli      407
Bernoulli, case      12 244 280
Bernoulli, extended      26
Bernoulli, law of large numbers      14 244 282
Berry      294 410
Bienayme      408
Bienayme, equality      12 246
Billingsley      196 409
Blackwell      369 411
Bochner      408 409
Bochner, theorem      220
Boltzmann      42 43
Bolzano — Weierstrass property      70
Borel(ian)      107 407 410
Borel(ian), Cantelli lemma      240
Borel(ian), cylinder      93
Borel(ian), field      93 104
Borel(ian), function      111 156
Borel(ian), functions theorem      156
Borel(ian), line      93 107
Borel(ian), sets      93 104
Borel(ian), space      93 107
Borel(ian), strong law of large numbers      18 19 26 244
Borel(ian), zero-one criterion      240
Bose — Einstein statistics      43 44
Bounded functional      80
Bounded Liapounov theorem      213 282
Bounded set      74
Bounded totally      75
Bounded variances      303
Bounded variances limit theorem      305
Bourbaki      407
Breiman      409
Brey      409
Brunk      271 410
Cantelli      20 240 409 410
Cantor theorem      74
Caratheodory extension theorem      88
Category, first      75
Category, second      75
Category, theorem      75
Cauchy mutual convergence criterion      74 104 114
Centering      244
Centering, at expectations      244
Centering, at medians      256
Centering, function      350
Central convergence criterion      323 326
Central inequalities      316
Central limit problem      302
Central limit theorem      321 322
Central statistical theorem      20
Chain      29
Chain, constant      29
Chain, elementary      29
Chain, stationary      39
Chained classes      28
Chained events      28
Chained random variables      29
Change of variable lemma      190
Characteristic function(s)      198
Characteristic function(s), and dichotomy      386
Characteristic function(s), composition theorem      226
Characteristic function(s), continuity theorem      204 224
Characteristic function(s), convergence criterion      204
Characteristic function(s), extension theorem      224
Characteristic function(s), general properties      207
Characteristic function(s), infinitely decomposable      306
Characteristic function(s), integral      202
Characteristic function(s), inversion formula      199
Characteristic function(s), self-decomposable      334
Characteristic function(s), stable      338 363
Characteristic function(s), triangular      386
Characteristic function(s), uniform convergence theorem      204
Chung      407 409 410
Chung and Fuchs      368 383 411
Chung and Ornstein      383 411
Class, closed under      59
Class, lower      272
Class, monotone      60
Class, of sets      55
Class, upper      272
Classical degenerate convergence criterion      290
Classical limit problem      286
Classical normal convergence criterion      292
Closed class of states      36
Closed model      22
Closed set      66
Closure theorem, infinitely decomposable laws      309
Combinatorial lemma      378
Combinatorial method      47
Compact, locally      71
Compact, set      69
Compact, space      69
Compactification      71
Compactness theorem for distribution functions      181
Compactness theorem for metric spaces      76
Compactness theorem for separated spaces      70
Compactness, properties      70
Compactness, relative      195
Compactness, relative, criterion      195
Comparison, convergences theorem      117
Comparison, lemma(s)      303 320
Complement      4 56
Complete convergence      180
Complete convergence criterion      204
Complete measure      91
Complete metric space      74
Completeness theorem, $L_{r^-}$      163
Completion of $\sigma$-field      91
Completion of a metric space      77
Complex random variable      154
composition      204 283
Composition and decomposition theorem      283
Composition, lemma      227
Composition, theorem      206
Compound(s), $\sigma$-field      237
Compound(s), Poisson      347
Compound(s), theorem      237
Conditional expectation      24
Conditional probability      24
Conditional regular probability      138
Consistency theorem      94
Consistent      93
Constant chain      29
Continuity, additive set functions—theorem      85
Continuity, characteristic functions theorem      204 224
Continuity, F- , interval      187
Continuity, P- , set      189
Continuous, F-function      67
Continuous, F-functional      80
Continuous, P-set function      85
Convergence criterion(ria), almost everywhere      116
Convergence criterion(ria), central      323 327
Convergence criterion(ria), complete      204
Convergence criterion(ria), degenerate      290 329
Convergence criterion(ria), iid central      348
Convergence criterion(ria), normal      292 328
Convergence criterion(ria), Poisson      308 329
Convergence criterion(ria), pr.’s on metric space      190
Convergence criterion(ria), tidy      346
Convergence criterion(ria), weak      203
Convergence theorem(s), $L_{r^-}$      165
Convergence theorem(s), comparison      117
Convergence theorem(s), dominated      126
Convergence theorem(s), Fatou — Lebesgue      12
Convergence theorem(s), moments      186
Convergence theorem(s), monotone      125
Convergence theorem(s), of types      216
Convergence theorem(s), uniform      204
Convergence, almost everywhere      114
Convergence, almost sure      153
Convergence, almost uniform      140
Convergence, complete      180
Convergence, essential      262
Convergence, in quadratic mean      260
Convergence, in rth mean      159
Convergence, of sequences of sets      58
Convergence, of types      216
Convergence, uniform      114
Convergence, weak      180
Convex function      161
Correspondence, lemma      344
Correspondence, theorem      97
Countable(ly)      16
Countable(ly), base      72
Countable(ly), class      57
Countable(ly), set      57
Countable(ly), set operations      57
Countable(ly), valued      64 106
Covering, open      69
Covering, rule      16
Cramer      271 408 409
Cylinder, Borel      62
Cylinder, product      62
Daniell      94 408
Decomposable infinitely      308
Decomposable self-      334
Decomposition theorem(s), chains      37
Decomposition theorem(s), composition and, theorem      283
Decomposition theorem(s), degenerate type      283
Decomposition theorem(s), distribution functions      178 200
Decomposition theorem(s), Hahn      87
Decomposition theorem(s), Lebesgue      131
Decomposition theorem(s), normal type      283
Decomposition theorem(s), Poisson type      283
Degenerate, characteristic function      215
Degenerate, convergence criterion      290 329
Degenerate, distribution function      215
Degenerate, law      215
Degenerate, random time      376
Degenerate, random variable      215
Degenerate, random walk      370
Degenerate, type      215
Dense set      72
Dense set, nowhere      75
Denumerable      16
Denumerable, class      57
Denumerable, set      57
Denumerable, set operations      57
Denumerable, valued      64 106
Diameter of a set      74
Dichotomy      380
Dichotomy, criterion      382
Difference equations      48
Difference of sets      56
Difference proper      56
Direction(ted)      67
Direction(ted), set      68
Dirichlet      187
Disjoint, class      57
Disjoint, events      4
Disjoint, sets      57
Distance of points      73
Distance of points and sets      78
Distance of sets      77
distribution      168 172 175
Distribution, $L_{d^-}$      370
Distribution, empirical distribution function      20
Distribution, function      20 96 169 177
Distribution, invariant      39
Distribution, probability      168
Doblin      30 302 354 403 410 411
Domain      62 108
Domain of attraction      360
Domain of attraction, partial      401
Domain of attraction, standard      402
Dominated Convergence Theorem      126
Doubrovsky      408
Duality rule      57
Dugue      409
Dunford      408
Egorov theorem      141
Einstein      43 44
Elementary chain      29
Elementary function      64 107
Elementary probability field      16
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