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| Авторизация |
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| Loeve M. — Probability Theory (part 2) |
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| Предметный указатель |
Extended Borel space 93 107
Extended Borel strong law of large numbers 26
Extended central convergence criterion 326
Extended central lemma 208
Extended central limit theorem 322
Extended convergence criterion 306
Extended Helly — Bray lemma 183
Extended identities 395
Extended infinitesimal operator 366 368
Extended Kolmogorov inequality 52
Extended Levy inequality 51
Extended norms ergodic theorems 109
Extended transition probabilities differentiation theorems 319 320
Extension 88
Extension lemma(s), decomposability 218
Extension lemma(s), jump processes 370
Extension lemma(s), Markov 318
Extension lemma(s), rightcontinuous stable processes 371
Extension of characteristic functions 225
Extension of linear functional 81
Extension of measures 88 194
Extension of submartingales 206
Extension theorem(s), C- 343
Extension theorem(s), characteristic functions 225
Extension theorem(s), linear functionals 81
Extension theorem(s), measures 88
Extension theorem(s), random functions 146
Extension theorem(s), random functions continuity 177
Extension theorem(s), translations 97
Factorization(s), extreme 396
Factorization(s), sample space 392 396
Factorization(s), theorem 11
Factorization(s), unique—theorem 389
Fatou — Lebesque convergence theorem 126
Feller 34 292 302 353 354 369 371 383 407 409—411 161 288 374 388
Fermi — Dirac statistics 42 43
Field(s) 59
Field(s) of outcomes 4
Field(s),  - 59
Field(s), Borel 93 104
Field(s), compound 156
Field(s), Lebesgue 129
Field(s), probability 8
Field(s), product 61 62
Field(s), separable 21
Finetti, de 302 411 31 66 212
Finite intersection property 70
Finite interval lemma 397
Finitely-valued 64 106
First category 75
First exit times 255
First hitting times 256
First kind discontinuity 176
First limit theorems 282
Fixed discontinuities 167
Fortet 409 289 386
Forward equation 311
Frechet 187 408 409
Freedman 237 264 386
Fubini theorem 136
Function(s) of function 64 106
Function(s), additive set 83
Function(s), almost everywhere Borel random 169
Function(s), almost surely equal random 165
Function(s), Baire 111
Function(s), Borel 113
Function(s), Borel random 168
Function(s), centering 350 220
Function(s), characteristic 199 202
Function(s), conditional distribution 26
Function(s), continuous 67
Function(s), convex 161
Function(s), countably-valued 64 106
Function(s), decomposable random 212
Function(s), denumerably-valued 64 106
Function(s), distribution 20 96 169 177
Function(s), domain of 62 107
Function(s), elementary 64 107
Function(s), equivalent 114
Function(s), F-continuous 187
Function(s), finite 105
Function(s), finitely-valued 64 106
Function(s), hermitian 132
Function(s), inverse 63 106
Function(s), measurable 65 107
Function(s), negative part of 105
Function(s), nonnegative definite 219
Function(s), nonnegative definite type 132
Function(s), numerical 105
Function(s), P-continuous 187
Function(s), positive part of 105
Function(s), random 152 156 163 164
Function(s), range of 63
Function(s), range space 62 105
Function(s), regular Markov 296
Function(s), second order random 131
Function(s), second order stationary 148
Function(s), separable random 171
Function(s), simple 64 107
Function(s), stationary random 169 303
Function(s), tail 229
Functional(s) 80
Functional(s), bounded 80
Functional(s), continuous 80
Functional(s), limit laws criterion 268
Functional(s), linear 80
Functional(s), normed 80
Gambler's ruin 48
Generator,  -weak 338
Generator, strong 337
Geometric probabilities 49
Gikhman and Skorohod 386
Glivenko 408
Glivenko — Cantelli 21
Gnedenko 302 354 407 409 411
Gumbel 45
H-convergence 349
hadamard 30 350
Hahn and Rosenthal 408
Hahn decomposition theorem 87
Halmos 196 408
Halmosand Savage 384
Harmonic orthogonal decomposition 149
Harmonizability theorem 142
Harmonizable covariance 140
Harmonizable second order random function 140
Hartman 77 385
Hartman and Wintner 278
Hausdorff 408
Hausdorff space 68
Heine — Borel property 70
Helly 386
Helly — Bray lemma 182
Helly — Bray lemma, extended 183
Helly — Bray lemma, generalized 187
Helly — Bray theorem 184
Herglotz lemma 220
Hermite(tian) 132 236
Hewitt — Savage 374 411
Hewitt — Savage, zero-one law 374
Hilbert space 80
Hille 237 344 386
Hitting time 377
Hitting time lemma 374
Hoelder inequality 158
Hopf 76 384
Hunt 289 383 388
Hurwicz 76 385
Huygens principle 28
Identification property 73
| Image, inverse, of a class 63 106
Image, inverse, of a set 63 106
Impossible event 4 54
Improper integral 130
Inclusion and closure lemma 338
Increments inequality 208
Increments, orthogonal 145
Indecomposability theorem 101
Indecomposable class of states 36
Indecomposable sequence 89
Indecomposable translation 101
Independence 11 235
Independence, asymptotic 42
Independence, conditional 16 290
Independent -fields 236
Independent classes 11 235
Independent events 11 235
Independent random functions 237
Independent random variables 11 237
Independent random vectors 237
Independent trials 7
Indicator(s) 59
Indicator(s) method 44
Induced -fields 64
Induced partition 64 106
Induced probability space 168 171
Induced topology 66
Inequality(ties),  - 157
Inequality(ties), basic 159
Inequality(ties), central 316
Inequality(ties), conditional 14
Inequality(ties), crossings 57 202
Inequality(ties), extrema 243
Inequality(ties), Hoelder 158
Inequality(ties), increments 208
Inequality(ties), Inequality(ties), basic ergodic 71
Inequality(ties), integral 208
Inequality(ties), Kolmogorov 25 247 275
Inequality(ties), Levy 259
Inequality(ties), Liapounov 174
Inequality(ties), Markov 160
Inequality(ties), Minkowski 158
Inequality(ties), Rademacher 123
Inequality(ties), Schwarz 158
Inequality(ties), submartingales 57
Inequality(ties), symmetrization 259
Inequality(ties), Tchebichev 11 160
Inequality(ties), truncation 209
Inequality(ties), weak symmetrization 258
Inferior limit 58
Infimum 56 103
Infinite decomposability 308
Infinite numbers 103
Infinitely often 241
Infinitesimal operator, -weak 338
Infinitesimal operator, extended 366 368
Infinitesimal operator, strong 337
Infinitesimal operators criterion 345
Infinitesimal operators criterion, corollary 345
Infinitesimal operators criterion, Markov 348
Initial distribution 296
Instantaneous state 314
Integrable 119
Integrable, -weakly 333
Integrable, positively 208
Integrable, sample 167
Integrable, strongly 332
Integrable, uniformly 164
Integral(s) in quadratic mean 138
Integral(s), Daniell 146
Integral(s), Darboux — Young 144
Integral(s), definitions 119
Integral(s), improper 130
Integral(s), iterated-theorem 137
Integral(s), Kolmogorov 145
Integral(s), Lebesgue 129 143
Integral(s), Riemann 129
Integral(s), Riemann — Stieltjes 129
Integral(s), second order 138
Integral, characteristic function 202
Integral, decomposition theorem 229
Integral, inequality 208
Integral, representation theorem 166
Integration by parts lemma 358
Integration in quadratic mean criterion 138
Integration lemma 227
Integration, restricted-theorem 20
Interior 66
Interior point 66
Intermediate Value Theorem 102
Intersection(s) 4 56
Intersection(s), finite-property 70
Interval(s) 61 62 104
Interval(s), finite-lemma 397
Invariance and continuity lemma 352
Invariance lemma 33
Invariance Theorem 39
Invariant -field 79
Invariant Banach subspace 336
Invariant Borel sets 91
Invariant distribution 39 33
Invariant events 79
Invariant functions 79
Invariant integral 83
Invariant probability 39 99
Invariant probability lemma 99
Invariant transition probability theorem 91
Invariant under translations 91
Inverse function 63 106
Inverse image 63 106
Inversion formula 199
Inversion of covariances 141
Inversion of random functions 141
Isolated jump(s), theorem 326
Isolated jump(s), time lemma 327
Iterated integrals theorem 147
Iterated logarithm, law of the 219 249 216
Iterated regular conditional probability theorem 138
Ito 226 289 388
Ito and McKean 237 386
Jump(s), discontinuity 176
Jump(s), isolated—theorem 326
Jump(s), isolated—time lemma 327
Jump(s), number of—lemma 226
Jump(s), Poisson sample—lemma 224
Jump(s), processes 369
Jump(s), processes extension lemma 370
Jump(s), time 327
Kac 407 410 263
Kaczmarz 384
Kakutani 106 385
Kallenberg 386
Karamata 354
Karamata, main theorem 356
Karhunen 385
Katz 411
Kawata 210 409
Kelley 408
Kemperman 369 393 395 410
Kendall 312 388
Kernel of a transformation 114
Kernel, reproducing 156
Khintchine 28 302 410 76 130 237 385 387
Khintchine, measure 343
Khintchine, representation 343
Kolmogorov 30 94 302 407 408 410 263 237 385 387 388
Kolmogorov approach 145
Kolmogorov equation 295
Kolmogorov equation, strong 309
Kolmogorov inequalities 25 247 275 44
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