Billingsley P. — Probability and Measure :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Billingsley P. — Probability and Measure

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

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:

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

Предметный указатель

Integral with respect to Lebesgue measure      224
Integrals of derivatives      433
Integration by parts      239
Integration over sets      215
Integration with respect to a density      217
Interarrival time      322
Interior      A11
interval      A9
Invariance principle      547 37.14
Inventory      323
Inverse image      A7 182
Inversion formula      355
Irreducible chain      117
Irregular paths      530
Iterated integral      237
Jacobian      229 253 266
Jensen's inequality      75 5.7 5.8 283 21.7 470
JORDAN      3.15
Jordan decomposition      442
k-dimensional Borel set      155
k-dimensional Lebesgue measure      171 178 20.4
Kac      413 610
Kahane      22.12
Khinchine      1.10 27.17
Khinchine — Pollaczek formula      332 333
Kindler      11.12
Kolmogorov      28.4
Kolmogorov's existence theorem      272 510 523 37.1
Kolmogorov's inequality      296 487
Kolmogorov's zero-one law      57 294 22.13
Kronecker's theorem      338
Kurzweil integral      17.13
Ladder height      325
Ladder index      325
Landau notation      A18
Laplace distribution      358
Laplace transform      285 293
Large deviations      145 149 27.17
Lattice distribution      26.1
Law of Large Numbers, strong      9 11 58 80 6.8 127 290 27.20
Law of large numbers, weak      5 11 58 81 292
Law of random variable      189 261
Law of the iterated logarithm      151
Lebesgue      15.5 213
Lebesgue decomposition      435 31.20 446 32.7
Lebesgue function      31.3
Lebesgue integrable      224
Lebesgue integral      224 225 229
Lebesgue measure      24 33 40 166 171 178 17.17.241 20.4
Lebesgue set      40 3.14 433
Lebesgue's density theorem      31.9 35.15
Leibniz's formula      17.10
Levy distance      14.9 25.4
Likelihood ratio      483 495
Limit inferior      46 4.2
Limit of sets      47
Limit superior      46 4.2
Lindeberg condition      369 27.7
Lindeberg theorem      368 30.1
Lindeberg — Levy theorem      366
Linear Borel set      155
Linearity of expected value      71
Linearity of the integral      209
Linearly independent reals      14.11 30.8
Lipschitz condition      31.17
Log-normal distribution      407
Lower integral      207
Lower semicontinuous      29.1
Lower variation      442
Lusin's theorem      17.8
Lyapounov's condition      371 27.7
Lyapounov's inequality      76 283
Lyapounov's theorem      371
m-dependent      6.11 376
M-test      A28 213
Mac Lane      173
Mapping theorem      343 391
Marginal distribution      266
Markov chain      107 20.8 375 379 29.18 450
Markov process      107 456 537
Markov time      130
Markov's inequality      74 283 34.9
Martingale      98 7.8 445 480 487 540 37.17
Martingale central limit theorem      497
Martingale convergence theorem      490
Maximal inequality      296 525
Maximal solution      119
Mean value      70 26.17
Measurable function      183
Measurable mapping      182
Measurable process      529 37.6 37.7
Measurable random variable      64
Measurable rectangle      234
Measurable set      18 34 163
Measurable space      158
Measurable with respect to a $\sigma$ -field      64 260
Measure      20 157
Measure space      21 158
Method of moments      405 30.5 30.6
Minimal solution      8.13
Minimum — variance estimation      475
Minkowski's inequality      5.10 5.11 21.24
Mixing      375 29.17 34.16
moment      71 281
Moment generating function      1.7 142 285 292 408
Monotone      22 159 162 209
Monotone class      39 3.10
Monotone class theorem      39
Monotone Convergence Theorem      211 214 34.8
Monotonicity of the integral      209
Multidimensional central limit theorem      398 29.18
Multidimensional characteristic function      395
Multidimensional distribution      265
Multidimensional normal distribution      397 29.5 29.10 33.8
Multinomial sampling      29.14
Negative part      203 259
Negligible set      8 1.4 1.12 41
Newton      17.11
Nonatomic      2.17
Nondegenerate distribution function      195
Nondenumerable probability      552
Nonmeasurable set      41 4.13 12.4
Nonnegative series      A25
Normal distribution      263 264 273 20.19 20.22 281 286 354 358 366 28.13 28.14 397
Normal number      8 1.9 1.11 3.15 81 6.13
Normal number theorem      9 6.9
Nowhere dense      A15
Nowhere differentiable      31.18 532
Null persistent      127
Number theory      412
Open set      A11
Optimal policy      99
Optimal stopping      130
Optimal strategy      134
Optional stopping      495 35.20
Order of dyadic interval      4
Order statistic      14.7
Orthogonal transformation      173 398
Outer boundary      58 85
Outer measure      33 3.2 162
P*-measurable      34
Pairwise additive      11.6
Pairwise disjoint      A3
Partial information      52
Partial summation      18.19
Partial-fraction expansion      20.20
Partition      A3 422 450
Pascal distribution      199
PATH function      320 518 525
Payoff function      131

Perfect set      A15
Period      122 8.27
Permutation      67 6.3 371
persistent      114 117 118
Phase space      108
Pinsky      27.17
Poincare      29.15
Point      16
Point of increase      12.9 20.16
Poisson approximation      312 336
Poisson distribution      262 20.18 286 310 23.13 27.1 27.3 387 28.12
Poisson process      307 449 457 33.7 34.12 36.12 36.14 560
Poisson's theorem      6.5
Policy, gambling      96
Polya's criterion      26.3
Polya's theorem      115 118
Positive part      203 259
Positive persistent      127
Power series      A29
Prekopa's theorem      314
Prime number theorem      5.17
primitive      227 419
Probability measure      20
Probability measure space      21
Probability transformation      14.4
Product measure      12.13 234 236
Product space      234 508 37.2 562
Progress and pinch      7.7
Proper difference      A1
Proper subset      A1
Queue size      333
Queueing model      121 124 322
Rademacher functions      5 1.8 63 298 301
Rado      19.8
Radon — Nykodym derivative      443 445 32.6 32.13 482 494 35.13
Radon — Nykodym theorem      443 32.4
Random Taylor series      301
Random variable      63 183 259
Random vector      184 260
Random walk      109 325
Rank of dyadic interval      4
Ranks and records      20.11
Rate of Poisson process      310
Rational rectangle      155
Realization of process      518
Record values      20.12 21.4 27.8
rectangle      A16 155
Rectifiable curve      19.3 31.11
Recurrent event      8.19
Red-and-black      88
Regular partition      178
Regularity      41 174
Relative measure      25.17
Renewal theory      8.19 321
Renyi — Lamperti lemma      6.15
Reversed martingale      492
Riemann integral      2 25 202 224 17.6 25.14
Riemann — Lebesgue lemma      354
Right continuity      175 261
Rigid transformation      173
Ring      11.5
Royden      1.13
Rudin      229 26.19 421 435
Saks      610
Saltus      189 309
Sample function      518
Sample path      320 518
Sample point      16
Sampling theory      410
Samuels      34.19
Scheffe's theorem      218 16.15
Schwarz's inequality      75 5.6 283
Second Borel — Cantelli lemma      55 4.14 83
Second category      A15
Second-order Markov chain      8.31
Secretary problem      111
Section      235
Selection problem      110 135
Selection system      91 93 7.3
Semicontinuous      29.1
Semiring      164
Separable $\sigma$ -field      2.10
Separable function      552
Separable process      553 558
Separant      553
Sequence space      2.16 4.18 8.4 36.6
Service time      322
Set      A1
Set function      20 440 32.11
Shannon's Theorem      6.14 8.30
Signed measure      32.12
Simple function      185
Simple random variable      63 185 260
Singleton      A1
Singular function      427 431 31.1
Singular part      446
Singularity      442 494
Skorohod embedding      339 545
Skorohod's theorem      342 392 399
Source      6.14 8.30
Southwest      176
Space      A1 16
Square-free integers      4.21
Stable law      389 28.15
Standard normal distribution      263
State space      108
Stationary distribution      121
Stationary increments      523 37.3
Stationary probabilities      121
Stationary process      36.2
Stationary sequence of random variables      375
Stationary transition probabilities      108
Statistical inference      91 148
Steiner symmetrization      251
Stieltjes integral      230
Stirling's formula      5.17 18.21 27.18
Stochastic arithmetic      2.15 4.21 5.16 5.17 6.17 18.18 25.15 412 30.10 30.11 30.12
Stochastic matrix      109
Stochastic process      309 319 506
Stopping time      96 130 486 534 536 539
Strong Law of Large Numbers      9 11 58 80 6.8 127 290 27.20
Strong Markov property      535 537 37.10
Strong semiring      11.6
Sub- $\sigma$ -field      52 260
Subadditivity, countable      23 159
Subadditivity, finite      22 159
Subfair game      88 99
Subfield      52 260
Submartingale      484 35.6
Subset      A1
Subsolution      8.6
Substochastic matrix      118
Sufficient $\sigma$ -field      471 34.20
Sufficient statistic      472
Superharmonic function      131
Supermartingale      485
Support line      A33
Support of measure      21 158 12.9 261 430 442
Surface area      247 19.8 19.13
Symmetric difference      A1
Symmetric random walk      109 115 135 35.10
Symmetric stable law      28.15
system      108
Tail $\sigma$ -field      57 295
Tail event      57 295 304
Taylor series      A29 301
Thin cylinders      36.6
Three series theorem      299
Tightness      346 392 29.3
Timid play      105

1 2 3

О проекте