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Язык: 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 Предметный указатель -inequality      157 , completeness theorem      163 , convergence theorem      164 , spaces      162 -measurable      88 -additive      83 111 -field(s)      59 -field(s), compound      156 235 -field(s), independent      236 -field(s), induced      64 -field(s), product      61 62 -field(s), tail      241 Abel theorem      400 Addition Property      10 Additive set function      83 Additive set function, -additive      83 111 Additive set function, -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, 163 Completion of -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), -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), 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, 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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