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| Авторизация |
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| Поиск по указателям |
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| Loeve M. — Probability Theory (part 2) |
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| Предметный указатель |
Kolmogorov strong law of large numbers 251
Kolmogorov three series criterion 249
Kolmogorov zero-one law 241 66.
Kronecker lemma 250
KRYLOV 110
Lambert 46
Langevin 236
Laplace 22 281 286 287 407
Law of large numbers, Bernoulli 14 26 244 282 11
Law of large numbers, Borel strong 18 19 26 244 11
Law of large numbers, classical 290
Law of large numbers, Kolmogorov strong 251
Law(s) 174
Law(s) of the iterated logarithm 219 249 276
Law(s), degenerate 215 281
Law(s), equivalence lemma 290
Law(s), equivalent sequences 39
Law(s), infinitely decomposable 308
Law(s), normal 213 281
Law(s), Poisson 282
Law(s), probability 174 214
Law(s), self-decomposable 334
Law(s), stable 326 363
Law(s), types of 215
Law(s), universal 403
Law(s), weighted 44
Law(s), zero-one 241 374 64 233
Le Cam 93 409 237 263
Le Cam extension of Donsker and Kolmogorov theorem 286
Le Cam Note by 286—287
Lebesgue 408
Lebesgue approach 143
Lebesgue decomposition theorem 131
Lebesgue field 129
Lebesgue integral 29
Lebesgue measure 128
Lebesgue sets 129
Lebesgue — Stieltjes field 128
Lebesgue — Stieltjes integral 128
Lebesgue — Stieltjes measure 128
Leeuvenhoek 239
Levy, P. 199 204 301 408 410 54 63 64 65 161 188 193 210 237 384 386
Levy, P., centering function 350
Levy, P., continuity theorem 204
Levy, P., demon 188
Levy, P., function 364
Levy, P., inequalities 259
Levy, P., measure 343
Levy, P., representation 343
Liapounov 411
Liapounov inequality 172
Liapounov theorem 213 287 289
Limit of a sequence of functions 113
Limit of a sequence of laws 214
Limit of a sequence of numbers 104
Limit of a sequence of sets 58
Limit problem, central 302
Limit problem, classical 286
Limit(s) of a directed set 68
Limit(s), along a direction 68
Limit(s), inferior 58
Limit(s), one-sided, of random functions 174 175
Limit(s), sample lemma 361
Limit(s), superior 58
Lindeberg 292 411
Line, Borel 93 107
Line, extended real 104
Line, real 93 103
Linear closure 79
Linear functional 80
Linear mapping 102
Linear mappings lemma 79 102
Linear space 70
Linear transformation 107
Linearly ordered 67
Locally compact 71
Lomnicki 409
Lower class 272
Lower variation 87
Lukacz 408
Lusin's theorem 140
Mappings, bounded 102
Mappings, linear 102
Mappings, nonnegative 102
Mappings, norm of 102
Marcinkiewicz 225 254 302 409 167
Marczewski 385
Markov(ian) 407 288 290
Markov(ian) chain 28 18 31
Markov(ian) dependence 18 28
Markov(ian) endomorphisms 299 334
Markov(ian) endomorphisms criterion 335
Markov(ian) equivalence theorem 289
Markov(ian) inequality 160
Markov(ian) infinitesimal operators criterion 348
Markov(ian) process 164 288 294
Markov(ian) process, regular 164 294 297
Markov(ian) process, stationary 293 302
Markov(ian) property 281
Markov(ian) property, strong 304 308 357
Markov(ian) sample rightcontinuity theorem 347
Markov(ian) semi-groups 331 335
Markov(ian) semi-groups criterion 336
Markov(ian) semi-groups unicity theorem 341
Markov(ian) stationarity theorem 299
Markov(ian) time 301
Markov(ian) time theorem 359
Markov(ian) time, stationary 307
Matrices, method of 48
Matrix, transition probability 29
Maxima times 376
Maximum times 393
Maxwell demon 188
Maxwell — Boltzmann statistics 42 43
Mean, quadratic 248 122 135
Mean, r-th 159
Measurability lemma 169
Measurability theorem 108 178
Measurable function 107
Measurable random function 168
Measurable sample- 167
Measurable sets 60 64 107
Measurable space 60 64 107
Measurable transformation 46
Measure(s) 84 112
Measure(s) space 112
Measure(s), convergence in 116
Measure(s), extension of 88
Measure(s), extension of—lemma 194
Measure(s), Lebesgue 129
Measure(s), Lebesgue — Stieltjes 128
Measure(s), normed 90 151
Measure(s), outer 88
Measure(s), outer extension 89
Measure(s), product 136
Measure(s), signed 87
Median 256
Median, centering at 256
Median, conditional 51
Metric compactness theorem 76
Metric linear space 79
Metric space 73
Metric topology 73
Meyer 193 383 386 388
Miller 76 385
Minimal class over 60
Minimal sufficient  -field 13
Minimality criterion 13
Minkowski inequality 158
Mixed conditional distribution 25
| Moment(s), convergence problem 187
Moment(s), convergence theorem 186
Moment(s), k-th 157 186
Moment(s), lemma 254
Moment(s), r-th absolute 157 186
Monotone class 60
Monotone Convergence Theorem 125
Monotone sequence of sets 58
Montmort 46
Moving discontinuities 147
Multiplication lemma 238
Multiplication property 11
Multiplication rule 24
Multiplication theorem 238
Mutual convergence 74 103 113 153
Nagaev 384
Negligibility, uniform asymptotic 302 314
Negligibility, uniform asymptotic, conditional 47
Neighborhood 66
Nelson 236 386
Neumann, von, theorem 76 385
Neveu 289 386
Neyman 407 11
Nikodym 133 408
No return state 31
Nondecreasing sequence 58
Nonhereditary systems 28
Nonincreasing sequence 58
Nonrecurrent state 31
Norm of a functional 79
Norm of a mapping 79 102
Norm, Hilbert 80
Normal approximation lemma 241
Normal approximation theorem 320
Normal continuous decomposable criteria 223
Normal continuous decomposable process 222
Normal convergence criterion 307
Normal convergence criterion, classical 292
Normal decomposition theorem 283
Normal law 213 281
Normal stability theorem 151
Normal strongly 128 133
Normal type 283
Normal, weighted 45
Normalized covariance 140
Normalized distribution function 199
Normalized random function, second order 140
Normed functional 80
Normed linear space 79
Normed mapping(s) 102
Normed measure 91 151
Normed sums 331
Norms ergodic lemma 108
Norms ergodic theorem 109
Nowhere dense 75
Null set 91 112
Null state 32
Null, preserving translation 103 108
Number of jumps lemma 226
Numerical function 105
Open covering 69
Open set 66
Operator(s),  -weak infinitesimal 338
Operator(s), diffusion 372
Operator(s), extended infinitesimal 366 368
Operator(s), one-dimensional diffusion 374
Operator(s), stationary transition 303
Operator(s), strong infinitesimal 337
Operator(s), transition 297
Operators criterion, infinitesimal 345
Operators criterion, Markov infinitesimal 341
Operators theorem, diffusion 375
Operators theorem, one-dimensional diffusion 378
Ordering, partial 67
Ornstein 381 410 307
Ornstein and Uhlenbeck 236
Orthogonal decomposition, elementary 125
Orthogonal decomposition, harmonic 149
Orthogonal decomposition, proper 144
Orthogonal expansion theorem 143
Orthogonal increments 145
Orthogonal random variables 246 122
Outcome (s) 14
Outcome (s) of an experiment 4
Outcome (s), field of 4
Outer extension 89
Outer measure 88
Owen 411
Oxtoby 385
Paley 237 387
Parseval relation 386
Parzen 407
Perrin 235
petrov 410
Petrovsky 263
Physical statistics 42
Planck 44
Poincare 235
Poincare, recurrence theorem 28
Point differentiation lemma 313
Poisson compound 347
Poisson continuous decomposability criterion 223
Poisson continuous decomposable 273
Poisson convergence criterion 229 329
Poisson decomposable process 231
Poisson decomposition theorem 283
Poisson distribution of particles 234
Poisson law 282
Poisson sample jumps lemma 224
Poisson theorem 15
Poisson type 283
Pollaczec 394 396 400 411
Pollaczec — Spitzer identity 393 400
Pollard 34
Polya 368 409
Port 369 393 412
Positive part 105
Positive state 32
Possible state(s) 370
Possible value (s) 370
Possible values theorem 371
probability 5 8 16 91 151 152
probability distribution 168
Probability field 8
Probability law 214
Probability rule, total 24
Probability space 91 151 152
Probability space, induced 168
Probability space, product 92
Probability space, sample 168 29
Probability, conditional 6 24 3—7
Probability, convergence in pr. 153
Probability, convergence on metric spaces 189 190
Probability, invariant 39 99
Probability, product—theorem 92
Probability, stability in 244
Probability, stationary transition 301
Probability, sub 187
Probability, transition 29 32 90 295
Product, -field 61 62
Product, cylinder 62
Product, field 61 62
Product, measurable space 61 62 137
Product, measure 135
Product, measure theorem 136
Product, probability 92
Product, probability space 92
Product, probability theorem 92
Product, scalar 80 122
Product, set 61
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