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| Loeve M. — Probability Theory (part 1) |
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| Предметный указатель |
Measure, Lebesgue — Stieltjes 128
Measure, Levy 343
Measure, normed 91 151
Measure, outer 88
Measure, outer extension of 89
Measure, product 136
Measure, signed 87
Measure, space 112
Median 256
Median, centering at 256
Metric, compactness theorem 76
Metric, linear space 79
Metric, space 73
Metric, topology 73
Minimal class over 60
Minkowski inequality 158
Moment(s), convergence problem 187
Moment(s), convergence theorem 186
Moment(s), kth 157 186
Moment(s), lemma 254
Moment(s), rth absolute 157 186
Monotone class 60
Monotone Convergence Theorem 125
Monotone sequences of sets 58
Montmort 46
Multiplication, lemma 238
Multiplication, property 11
Multiplication, rule 24
Multiplication, theorem 238
Negligibility, uniform asymptotic 302 314
Neighborhood 66
Neyman 407
Nikodym 133 408
No-return state 31
Nonhereditary systems 28
Nonrecurrent state 31
Norm of a functional 79
Norm of a mapping 79
Norm, Hilbert 80
Normal approximation theorem 300
Normal convergence criterion 307
Normal decomposition theorem 283
Normal law 213 281
Normal type 283
Normalized distribution function 199
Normed functional 80
Normed linear space 79
Normed measure 91 151
Normed sums 331
Nowhere dense 75
Null set 91 112
Null state 32
Numerical function 105
Open covering 69
Open set 66
Ordering, partial 67
Orthogonal random variables 246
Outcome(s) 4
Outcome(s), field of 4
Outcome(s), of an experiment 4
Outer, extension 89
Outer, measure 88
Owen 411
Parseval relation 386
Parzen 407
petrov 410
Physical statistics 42
Planck 44
Poincare recurrence theorem 28
Poisson, compound 347
Poisson, convergence criterion 229 329
Poisson, decomposition theorem 283
Poisson, law 282
Poisson, theorem 15
Poisson, type 283
Pollaczec 396 394 400 411
Pollaczec — Spitzer identity 393 400
Pollard 34
Polya 368 409
Port 369 393 412
Positive part 105
Positive state 32
Positivity criterion 33
Possible state(s) 370
Possible value(s) 370
Possible values theorem 371
probability 5 8 16 91 151 152
Probability space 91 151 152
Probability space, induced 168
Probability space, product 92
Probability space, sample 168
Probability space, transition 29
Probability, conditional 6 24
Probability, convergence in 153
Probability, convergence on metric spaces 189 190
Probability, distribution 168
Probability, field 8
Probability, law 214
Probability, product-theorem 92
Probability, rule, total 24
Probability, stability in 244
Probability, sub 187
Probability, transition 29
Product,  -field 61 62
Product, cylinder 62
Product, field 61 62
Product, measurable space 61 62 137
Product, measure 136
Product, probability 92
Product, probability theorem 242
Product, scalar 80
Product, set 61
Product, space 61 62
Prohorov 190 193 264 409
Quadratic mean, convergence in 260
Radon — Nikodym theorem 133
Radon — Nikodym theorem, extension 134
Raikov 283 411
Random event 5 8
Random function 152 156
Random sequence 152 155
Random time 375
Random time identities 390
Random time translations 376
Random trial 6
Random variable 6 9 17 152
Random vector 152 155
Random walk 47 378 379
RANGE 63
Range, space 62 105
Ranked random variables 350
Ranked sums 405
Ray 369 395 412
Real line 93
Real line, extended 93 107
Real number 93
Real number extended 93
Real space 93
Recurrence 380
Recurrence, criterion 32
Recurrence, theorem(s) 27 384
Recurrent state(s) 31 380
Recurrent state(s), walk 28
Regular variation 354
Regular variation, criterion 354
Relative compactness 190
Relative compactness, theorem 195
Representation theorem 313
Representation theorem, integral 166
Restriction 88
| Return criterion 32
Return state 31
Riemann integral 129
Riemann — Stieltjes integral 129
Riesz, F. 222
rth absolute moment 157 186
rth mean 159
Ruin, gambler’s 48
Saks 408
Savage 374
Scalar product 80
Scheff 408
Schwarz inequality 158
Section 61 62 135
Self-decomposable (bility) 334
Self-decomposable (bility), criterion 335
Separable space 68
Separation theorem 68
Sequence(s), convergence equivalent 245
Sequence(s), random 152 155
Sequence(s), tail equivalent 245
Sequence(s), tail of 241
Series criterion, three 249
Series criterion, two 263
Set function, -additive 83 111
Set function, -finite 83 11
Set function, additive 83
Set function, continuous 85
Set function, countably additive 83
Set function, finite 82 111
Set function, finitely 83
Set(s), Borel 93 104
Set(s), bounded 74
Set(s), closed 66
Set(s), compact 69
Set(s), dense 72
Set(s), directed 68
Set(s), empty 4 54
Set(s), Lebesgue 129
Set(s), measurable 60 64 107
Set(s), null 91 112
Set(s), open 66
Set(s), product 61
Set(s), subdirected 69
Set(s), totally bounded 75
Shohat 187
Signed measure 87
Simple function 64 107
Simple random variable 6 152
Snell 66
Space, adjoint 81
Space, Banach 79
Space, Borel 93 107
Space, compact 69
Space, complete 74
Space, Hausdorff 68
Space, Hilbert 80
Space, induced probability 168
Space, linear 79
Space, measurable 60 64 107
Space, measure 112
Space, metric 73
Space, metric linear 79
Space, normal 78
Space, normed linear 79
Space, of sets 55
Space, probability 91 151 152
Space, product 61 62
Space, product measurable 61 62 137
Space, product measure 136
Space, product probability 91
Space, range 62 105
Space, sample probability 168
Space, separated 68
Space, topological 66
Sphere 73
Spitzer 369 393 394 404 410 412
Spitzer, basic identity 396
Spitzer, basic theorem 401
Stability, almost sure 244
Stability, almost sure criterion 264
Stability, and attraction criterion 364
Stability, in probability 244 246
Stable characteristic function 338
Stable law 338 363
State(s), closed class of 36
State(s), equivalent 36
State(s), everreturn 36
State(s), indecomposable class of 36
State(s), no return 31
State(s), nonrecurrent 31 380
State(s), null 32
State(s), period of 33
State(s), positive 32
State(s), possible 370
State(s), recurrent 31 380
State(s), return 31
State(s), transient 380
Stationary chain 39
Steinhaus 409
Stieltjes 128 129
Stochastic variable 174
Stochastically independent 11
Strong law of large numbers, Borel 18 19 26 244
Strong law of large numbers, Kolmogorov 241
Structure, corollary 348
Structure, theorem 310
Subspace, linear 79
Subspace, topological 66
Sum of sets 4 51
Superior limit 58
Supremum 56 103
Sure, almost 151
Sure, event 4 151
Symmetrization 257
Symmetrization, inequalities 259
Symmetrization, inequalities, weak 257
Tail, -field 241
Tail, equivalence 245
Tail, event 241
Tail, function 241
Tail, of a sequence 241
Tchebichev 409
Tchebichev, inequality 11 160
Tchebichev, theorem 287
Three alternatives 375
Three alternatives criteria 399
Three series criterion 249
Tight(ness) 194
Tight(ness), and relative compactness 195
Tight(ness), lemma 194
Tight(ness), theorem 194
Toeplitz lemma 250
Topological space 66
Topological subspace 66
topology 66
Topology, metric 73
Topology, reduced 66
Total(ly) bounded set 75
Total(ly) probability rule 24
Total(ly) variation 87
Transition probability 29
Trial(s), deterministic 5
Trial(s), identical 5 6
Trial(s), independent 5 6
Trial(s), random 6
Trial(s), repeated 5 6
Triangle property 73
Triangular characteristic function 386
Triangular probability density 386
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