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| Loeve M. — Probability Theory (part 1) |
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| Предметный указатель |
Elementary random variable 17 152
Empirical distribution function 20
Empty set 4 54
Equivalence, Andersen 377 393
Equivalence, Andersen, lemma 378
Equivalence, class 154
Equivalence, convergence 245
Equivalence, lemma, laws 290
Equivalence, lemma, series 245
Equivalence, tail 245
Equivalence, theorem (s) 263 379
Equivalent distribution functions 96
Equivalent functions 114
Equivalent random variables 154
Equivalent states 36
Erdos 34
Esseen 294 410
Essential convergence 262
Essential divergence 262
Euler 47
Events 3 8 151
Events, disjoint 3
Events, elementary 151
Events, exchangeable 45 21
Events, impossible 4 151
Events, independent 11 73 235
Events, null 152
Events, random 5 8
Events, sure 4 151
Events, tail 241
Everreturn state 36
Exchangeable events 45 373
Exchangeable random variables 373
Expectation of a random function 156
Expectation of a random sequence 154
Expectation of a random variable 10 17 153 154
Expectation, centering at 244
Expectation, criterion 384
Expectation, indefinite 153
Exponential Bounds 266
Exponential identities 388 396
Extended Bernoulli law of large numbers 26
Extended Borel line 93 107
Extended Borel space 93 107
Extended Borel strong law of large numbers 26
Extended central convergence criterion 326
Extended central limit theorem 322
Extended convergence criterion 306
Extended Helly — Bray lemma 183
Extended identities 395
Extension 88
Extension of characteristic functions 225
Extension of linear functionals 81
Extension of measures 88
Factorization(s), extreme 396
Factorization(s), sample space 392 396
Factorization(s), unique, theorem 389
Feller 34 292 302 353 354 369 371 383 407 409—411
Fermi — Dirac statistics 42 43
Field(s) 59
Field(s),  - 59
Field(s), Borel 93 104
Field(s), compound 156
Field(s), Lebesgue 129
Field(s), of outcomes 4
Field(s), probability 8
Field(s), product 61 62
Finetti, de 302 411
Finite intersection property 70
Finite intersection property, interval lemma 45
Finitely-valued 64 106
First category 75
First limit theorems 282
Fortet 409
Frechet 187 408
Fubini theorem 136
Function(s), additive set 83
Function(s), Baire 111
Function(s), centering 350
Function(s), characteristic 199 202
Function(s), continuous 67
Function(s), convex 161
Function(s), countably-valued 64 106
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), inverse 63 106
Function(s), measurable 65 107
Function(s), non-negative definite 219
Function(s), numerical 105
Function(s), of function 64 106
Function(s), P-continuous 187
Function(s), positive part of 105
Function(s), random 152 156
Function(s), range of 63
Function(s), range space 62 105
Function(s), simple 64 107
Function(s), tail 241
Functional 80
Functional, bounded 80
Functional, continuous 80
Functional, linear 80
Functional, normed 80
Gambler’s ruin 48
Geometric probabilities 49
Glivenko 408
Glivenko — Cantelli 21
Gnedenko 302 354 407 409 411
Gumbel 45
hadamard 30
Hahn and Rosenthal 408
Hahn decomposition theorem 87
Halmos 196 408
Hausdorff 408
Hausdorff, space 68
Heine — Borel property 70
Helly 409
Helly — Bray lemma 182
Helly — Bray lemma, extended 183
Helly — Bray lemma, generalized 187
Helly — Bray theorem 184
Herglotz lemma 220
Hewitt — Savage 374 411
Hewitt — Savage, zero-one law 374
Hilbert space 80
Hitting time 377
Hitting time, lemma 374
Holder inequality 158
Huygens principle 28
Identification property 73
Image, Inverse of a class 63 106
Image, Inverse of a set 63 106
Impossible event 4 110
Improper integral 130
Increments inequality 208
Indecomposable class of states 36
Indefinite expectation 154
Indefinite integral 130
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) 9 59
Indicator(s), method of 44
Induced -field 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), Holder 158
Inequality(ties), integral 208
Inequality(ties), Kolmogorov 25 247 275
Inequality(ties), Levy 259
Inequality(ties), Liapounov 177
Inequality(ties), Schwarz 158
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
Integrable 119
Integrable uniformly 164
Integral(s), Daniell 146
Integral(s), Darboux — Young 144
Integral(s), definitions 119
Integral(s), elementary properties 120
Integral(s), improper 130
Integral(s), iterated, theorem 137
Integral(s), Kolmogorov 145
Integral(s), Lebesgue 129 143
Integral(s), Lebesgue — Stieltjes 128
Integral(s), Riemann 129
Integral(s), Riemann — Stieltjes 129
Integral, characteristic function 202
Integral, inequality 208
Integral, representation theorem 166
Integration by parts lemma 358
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 Theorem 39
Invariant distribution 39
Inverse function 63 106
Inverse image 63 106
Inversion formula 199
Iterated logarithm, law of 219
Iterated regular conditional probability theorem 138
Kac 407 410
Karamata 354
Karamata, main theorem 356
Katz 411
Kawata 210 409
Kelley 408
Kemperman 369 393 395 410
Khintchine 28 302 410
Khintchine, measure 343
Khintchine, representation 343
Kolmogorov 30 94 302 407 408 410
Kolmogorov, approach 145
Kolmogorov, inequalities 25 247 275
Kolmogorov, strong law of large numbers 251
Kolmogorov, three series criterion 249
Kolmogorov, zero-one law 241
Kronecker lemma 250
Lambert 46
Laplace 22 281 286 287 407
Law of large numbers, Bernoulli 14 26 244 282
Law of large numbers, Borel, strong 18 19 26 244
Law of large numbers, classical 290
Law of large numbers, Kolmogorov, strong 251
Law(s) 174
Law(s), degenerate 215 281
Law(s), equivalence lemma 290
Law(s), infinitely decomposable 308
Law(s), normal 213 281
Law(s), of the iterated logarithm 219
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), zero-one 241 374
Le Cam 193 409
Lebesgue 408
Lebesgue — Stieltjes, field 128
Lebesgue — Stieltjes, integral 128
Lebesgue — Stieltjes, measure 128
Lebesgue, approach 143
Lebesgue, decomposition theorem 131
Lebesgue, field 129
Lebesgue, integral 129
Lebesgue, measure 128
Lebesgue, sets 129
Levy, P. 199 301 302 408 410
Levy, P., continuity theorem 204
Levy, P., function(s) 361
Levy, P., inequalities 259
Levy, P., measure 343
Levy, P., representation 343
Liapounov 411
Liapounov, inequality 174
Liapounov, theorem 213 287 289
Limit of a directed set 68
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, along a direction 68
Limit, inferior 58
Limit, superior 58
Lindeberg 292 411
Line, Borel 93 107
Line, extended real 104
Line, real 93 103
Linear closure 79
Linear functional 80
Linear space 70
Linearly ordered 67
Liouville theorem 369
Lomnicki 409
Lower, class 272
Lower, variation 87
Lukacz 408
Lusin theorem 140
Marcinkiewitz 225 254 302 409
Markov 407
Markov, chain 28
Markov, dependence 28
Markov, inequality 160
Matrices, method of 48
Matrix, transition probability 29
Mean rth mean 159
Measurable function 107
Measurable sets 60 64 107
Measurable space 60 64 107
Measure 84 112
Measure, convergence in 116
Measure, Khintchine 343
Measure, Lebesgue 129
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