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Billingsley P. — Probability and Measure
Billingsley P. — Probability and Measure

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Название: Probability and Measure

Автор: Billingsley P.

Аннотация:

A text that offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. The coverage extends to probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes. This edition features an improved version of Brownian motion and the replacement of queuing theory with ergodic theory.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 1986

Количество страниц: 622

Добавлена в каталог: 14.06.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\alpha$-mixing      375 29.17
$\epsilon -\delta$ definition of absolute continuity      443 32.3
$\lambda$-System      36 3.8 3.10
$\mu$-continuity set      344 390
$\mu$-measurable      163
$\pi - \lambda$ theorem      36 3.9
$\pi$-system      36 3.9
$\sigma$-field      17 19
$\sigma$-field generated by a class of sets      19
$\sigma$-field generated by a random variable      64 260
$\sigma$-field generated by a transformation      13.5
$\sigma$-finite measure      157 10.7
$\sigma$-finite on a class      158
$\sigma$-ring      11.5
${L}^{p}$-space      21.25
${L}_{1}$-bounded      504
A-distribution      194
Abel      244
Absolute continuity      434 436 31.7 442 443 32.3
Absolute moment      281
Absolutely continuous part      446
Absorbing state      109
Adapted a-fields      480
Additive set function      440 32.11
Additivity, countable      158
Additivity, finite      21 23 158
Algebra      17
Almost always      48
Almost everywhere      54 420
Almost surely      54
Amart      504
Aperiodic      122
Approximation of measure      166
ARC      19.3
Arc length      19.3 31.11
Area over the curve      74
Area under the curve      206
Arrival times      309
Asymptotic equipartition property      6.14 8.30
atom      20.16
Axiom of Choice      A8 18
Bahadur      9.4
Baire category      A15 1.13
Baire function      13—10
Bayes      59 33.9 33.17 496
Benford's law      25.3
Beppo Levi's theorem      16.9
Bernoulli trials      80 143 148 9.3 368
Bernoulli — Laplace model of diffusion      108
Bernstein polynomial      82
Bernstein's theorem      82
beta function      20.24
Betting system      95 485
Billingsley      19.12 392
Binary digit      3
Binary expansion      3
Binomial distribution      262
Binomial series      17.11
Birkhoff      42 173
Blackwell      476
Bold play      98
Boole's inequality      23
Borel      A13 9
Borel function      184 13.10 31.3
Borel set      20 3.14 155 433
Borel — Cantelli Lemmas      53 55 58 83 21.6 22.4
Borel's normal number theorem      9 6.9
Borel's paradox      33.1
Boundary      A11 265
Bounded convergence theorem      214
Bounded gambling policy      97
Bounded variation      435
Branching process      483
Britannica      1.5
Brown      314
Brownian motion      522 529 553 559 560
Burstin's theorem      22.16
Canonical measure      384
Canonical representation      384
Cantelli's inequality      5.5
Cantelli's theorem      6.6
Cantor function      31.2 31.15
Cantor set      1.6 1.9 3.16 423 12.8
Caratheodory's condition      168
Cardinality of $\sigma$-fields      2.11
Cartesian product      234
Category      A15
Cauchy distribution      20.20 21.5 22.6 358 26.9 28.5 28.13
Cauchy's equation      A20 14.11
Cavalieri's principle      18.8
Central limit theorem      300 366 27.14 27.15 387 398.408 34.17.497
Central symmetrization      251
Cesaro averages      A30 25.16
Change of variable      218 228 229 252 264 280
Characteristic function      A5 351 395
Chebyshev's inequality      5 75 5.5 81 283 34.9
Chernoff s theorem      147
Chi-squared distribution      20.22 21.35 29.14 462
Chi-squared statistic      29.14
Circular Lebesgue measure      13.19
Class of sets      16
Closed set      A11
Closed set of states      8.23
Closed support      12.9
Closure      A11
Cluster variable      35.23
Co-countable set      18
Cofinite set      18
Collective      7.3
Compact      A13
Complement      A1
Complete space or measure      39 10.6 533
Completely normal number      6.13
Completion      3.5 10.6
Complex functions, integration of      221
Compound Poisson distribution      28.3
Compound Poisson process      23.8
Concentrated      158
Conditional distribution      460 471 36.13
Conditional expected value      131 466 467 34.19
Conditional probability      46 448 451 454 33.5 33.13
Consistency conditions for finite-dimensional distributions      507
Content      3.15
Continuity from above      23 169 177 265
Continuity from below      23 159 265
Continuity of paths      524
Continuity set      344 390
Continuity theorem for characteristic functions      359 396
Conventions involving $\infty$      157 202
Convergence in distribution      338 390
Convergence in mean      21.22
Convergence in measure      274
Convergence in probability      274 299 340
Convergence of random series      298
Convergence of types      195
Convergence with probability      1 274 299
Convex functions      A32 75
Convolution      272
Coordinate function      509
Coordinate variable      509
Coordinate-variable process      510
Countable      8
Countable additivity      20 158
Countable subadditivity      23 159 162 164
Countably additive      20
Countably generated $\sigma$-field      2.10 20.1
Countably infinite      8
Counting measure      158
Coupled chain      123 8.16
Coupon problem      372
Covariance      284
Cover      A3
Cramer — Wold theorem      397 30.6
Cumulant      144
Cumulant generating function      144
Cylinder      2.16 509 36.6
Daniell — Stone theorem      11.12 16.25
Darboux — Young definition      208
Decomposition      A3
Definite integral      202 203
Degenerate distribution function      195
Delta method      368 27.10 27.11 402 29.8
DeMoivre — Laplace theorem      25.11 368
DeMorgan's law      A6
Dense      A15
Density of measure      216 440
Density of random variable or distribution      262 264 266
Density of set of integers      2.15
Density point      31.9
Denumerable probability      45 552
Dependent random variables      375
Derivates      423
Derivatives of integrals      421
Diagonal method      A14
Difference      A1
Difference equation      A19
Differential equations and the Poisson process      317
Dirichlet's theorem      A26 20
Discontinuity of the first kind      561
Discrete measure      21 158
Discrete random variable      261
Discrete space, l.l      21
Disjoint      A3
Disjoint supports      430 442
Distribution function      176 189 261 265 429
Distribution, of random variable      68 189 261
Distribution, of random vector      265
Dividing cake      2.18
Dominated Convergence Theorem      72 213 214 16.6 21.21 348
Dominated measure      442 472 494
Doob      18.11 490 35.19
Double exponential distribution      358
Double integral      237
Double series      A27
Double-or-nothing      95 7.6
Doubly stochastic matrix      8.22
Dubins — Savage theorem      99
Dyadic expansion      A31 3
Dyadic interval      4
Dyadic rational      4
Dynkin      110
Dynkin's $\pi -\lambda$ theorem      37
Egorov's theorem      13.13
Empirical distribution function      275
Empty set      A1
entropy      52 6.14 8.30 31.17
Equicontinuous      26.15
Equivalence class      52
Equivalent measures      442 472
Erdoes — Kac central limit theorem      413
Erlang density      23.2
Essential supremum      5.11
Estimation      475
Etemadi      290 297
Euclidean distance      A16
Euclidean space      A1 A16
Euler      18.17 18.22
Euler's function      2.15
Event      16
Excessive function      131 8.33
Existence of independent sequences      68 271
Existence of Markov chains      112
Expected value      70 280
Exponential convergence      128
Exponential distribution      191 263 20.25 286 307 327 331 358 28.5
Extension of measure      32 164 11.1 11.5
Extremal distribution      197
Factorization and sufficiency      472
Fair game      88 480 485
Fatou's lemma      212 16.4 34.8
Federer      19.8
Feller      1 8.19 108 25.3 25.11 610
Feller's theorem      374
Field      17 19 2.5
Finite additivity      21 23 158
Finite measure      157
Finite or countable      8
Finite subadditivity      22 159
Finite-dimensional distributions      319 506
Finite-dimensional sets      509
Finitely additive field      18
First Borel — Cantelli lemma      53
First category      A15 1.13
First passage      115
Fisher      199
Fixed discontinuity      314
Fourier series      361 26.26 27.21
Fourier transform      352
Fr6chet      199
frequency      5
Fubini's theorem      238 36.9
Functional central limit theorem      548
Fundamental in probability      20.28
Fundamental theorem of calculus      227 419
Galambos      199
Gambling policy      96
Gamma distribution      20.23 26.8 28.5
Gamma function      18.22
Generated $\sigma$-field      19 64 13.5 260
Glivenko — Cantelli theorem      275 25.2
Gnedenko      199 28.4
Goncharov's theorem      371
Hahn decomposition      441 32.2 34.19
Halmos      A8 39 11.6 610
Hamel basis      14.11
Hardy      1.10 413 564
Hardy — Ramanujan theorem      6.17 30.9 30.12
Hausdorff      174 564
Hausdorff dimension      19.11
Hausdorff measure      247
Heine — Borel theorem      A13 A17
Helly selection theorem      345 392
Hewitt — Savage zero-one law      304
Hilbert space      21.27 34.13 34.14 35.18
Hitting time      134 541 37.9
Holder's inequality      75 5.9 5.11 283 34.9
Hypothesis testing      148
Inadequacy of ${R}^{t}$      517 36.10
Inclusion-exclusion formula      22 159
Indefinite integral      419
Independent array      51
Independent classes      50
Independent events      48 453
Independent increments      309 522 37.3
Independent random variables      66 73 192 267 284 287 290 355 454
Independent random vectors      268 269 454
Indicator      A5
Infinite convolutions      26.22
Infinite series      A25
Infinitely divisible distributions      382 385
Infinitely often      47
Infinitesimal array      373
information      52
Information source      6.14 8.30
Initial digit problem      25.3
Initial probabilities      108
Inner boundary      58 85
Inner measure      33 3.2
Integrable      203
integral      202
1 2 3
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