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| Dudley R.M., Fulton W. (Ed) — Real Analysis and Probability |
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| Предметный указатель |
Disjoint 7 507
Distance from a set 60
Distribution functions 283
Distribution functions, convergence of 295—296 307 387 398 425
Distributions, conditional 342—347 350
Dixmier, J. 183
Dodd, B.E. 22
Domain: function 5 508
Domain: relation 8—9
Dominated convergence 132
Dominated convergence for conditional expectations 338 381
Doob, J.L. 275 381—382 480—482 540
Double induction 13
Double integrals 134—142
du Bois-Reymond, P. 246
Dual space of a normed space 190
Dual space of a normed space, dual of  208
Dual space of a normed space, dual of C(X ) 239—240
Dubins, L. 112 274 381 482
Dudley, R.M. 148 434—435 481 539—540
Dugac, P. 277
Dugundji, J. 79
Dunford, N. 78 219 277
Dyson, F. 435
Efimov, N, V. 330
Egoroff's theorem 243—244
Egoroff, D. 247
Ehrenfeucht, A. 275
Eichhorn, E. 76
Eidelheit, M. 219
Einstein, A. 480
Empirical distribution functions 400—401 460
Empirical measures 399
Empty set 4 506
Equicontinuous 51—52 396
Equicontinuous, uniformly 51—52
Equivalence: class 10
Equivalence: relation 10
Equivalence: theorem 16
Erdoes, P. 276
Ergodic theorems 267—273 277
Ergodic theorems, subadditive 374—381
Essentially bounded functions 155
Estimators 426
Etemadi, N. 276
Euclid 183 503
Euclidean metric 43
Euler, L. 184 331
Events 251
Expectation 251
Expectation of vector variable 306
Exponential distribution 315
Exponential of a measure 318—319
Extended real numbers ![$[-\infty, \infty]$](/math_tex/f1ebfca6e1399f1be5d4c66c868a884d82.gif) 72
Extension: continuous functions 63—67
Extension: continuous linear functions 191 218
Extension: Lipschitz functions 189 218
Extension: measurable functions 127
Extension: measures 89—92
Extension: signed measures 180—181
Extensionality 3—4 506
F-space 212
Fabian, V. 539
Family of sets 25
Fan, Ky 330
Fan, Ky, metric 289—291 330 397 407
Fatou's lemma 131 148
Fatou's lemma, conditional 340
Fatou, P. 148 184
Fedorchuk, V.V. 76
Feferman, S. 77
Fefferman, C. 246
Felix, L. 148 480
Feller, W. 254 273 318 332 482
Fenchel, W. 218
Fernique, X. 435
Filter (base) 29
Filtration 453
Finite-dimensional distributions 441
Finitely additive 85 94 273—274
First category 59
First-countable 31
First-order predicate logic 504—505
Fischer, E. 183—184
Fisz, M. 275
Formal system 503—505
Fortet, R. 433—434
Foundation, axioms of 517
Fourier series 171—173 184 240—243 246—247 314
Fourier transform 298—310 315 331—332
Fourier transform, inversion 303—305
Fourier, J.B.J. 246—247 481
Fraenkel, A. 22 505 517
Frechet, M. 75—76 78 111 184 330
Free variable (logic) 505
Frewer, M. 22
Fricke, W. 184
Friedman, H. 149
Frink, A.H. 79
Frolik, Z. 480
Fubini theorem 137 149
Fubini, G. 149
Full set 510
Function 5—6 508
Functional analysis 152—221
Fundamenta Mathematicae 518
Fundamental theorem of calculus 228—229
Furstenberg, H. 379
Game, fair or favorable 353 365
Gamma density and function 286
Garling, D.J.H. 246
Garsia, A. 277
Gauss, K.F. 331
Gaussian probability densities 138 299 331
Gaussian stochastic process 443
Generalized Continuum Hypothesis 515 518
Generated  -algebra 86
Generated -ring 118
Geometry of numbers 203 218
Gerstenhaber, M. 481
Getoor, R.K. 539
Gikhman, I.I. 332
Gilat, D. 382
Gini index 435
Glivenko — Cantelli theorem 400 434
Glivenko, V.I. 434
Gnedenko, B.V. 274 275 332
Godwin, H.J. 276
Goedel, K. 517—518
Gram — Schmidt orthonormalization 168 184
Gram, J.P. 184
Graph (function) 5
Grattan-Guinness, I. 75 246—247 481
Grebogi, C. 232
Greenleaf, F.P. 274
Group, topological 69 219 530
Gudermann, C.J. 77
Haar measure 530
Haar, A. 530
Haar, D. ter 277
Hadwiger, H. 219
Hagood, J.W. 184
Hahn decomposition 178—179 185
Hahn — Banach theorem 191 201—203 218 219
Hahn, H. 78 185 218—219
Hald, A. 332
Half-open intervals 25
Half-space 200
Hall, Marshall 434
Hall, Peter 328 332 382
| Hall, Philip 434
Halmos, P.R. 148 245—246 277—278 381 434 435 530
Hamel basis 168—169 214
Hammersley, J.M. 379
Hardy, G.H. 78 183 219 481
Hartman, P. 482—483
Hauey, R.J. 247
Haupt, O. 185
Hausdorff maximal principle 19—22
Hausdorff space 30 76
Hausdorff, F. 22 76—79 148 149 273 276 500
Hawkins, T. 111 148
Heat equation 138 481
Heijenoort, J. van 519
Heine — Borel theorems 76
Heine, H.Eduard 76 78
Heine, Heinrich 78
Helly — Bray theorem 387 434
Helly, E. 433
Hereditary collection of sets 105
Herivel, J. 247 481
Hewitt — Savage 0-1 law 272
Hewitt, E. 278
Heyde, C. 276 382
Hilbert spaces 160—174
Hilbert, D. 183—184 332
Hildebrandt, T.H. 219 433
Hitting time 453
Hoeffding, W. 435
Hoelder condition 56 433
Hoelder inequality 154 157 182—183 208
Hoelder, O. 182—183 381 433
Hoermander, L. 139 219
Hoffman, K. 308
Holomorphic function 523
Homeomorphism 40
Homological algebra 518
Hopf, E. 277
Hopf, H. 79
Hunt, G.A. 481—482
Hunt, R.A. 246
Hurwitz, A. 184
Hypergeometric probabilities 429
Hyperplane 199
i.i.d. (independent, identically distributed) 261
Image measure 121
imaginary numbers 521
In probability, convergence 261 287—291 295
Ince, E.L. 433
Includes 3
Indecomposable law 314
Independence (joint, pairwise) 252—253 452
Independence (joint, pairwise) of a -algebra 340 452
Indicator function 6 32 253
Indiscrete topology 39
Induction 12—13 513
Inductive set 12
Inequalities for integrals 152—157
Inf, infimum 8 34—35
Infinite sums of independent variables 320—325
Infinitely divisible laws 319 326—329
Infinitely often 262
Infinity, axiom of 507
Initial segment 13
Inner measure 105 533
Inner product 160—162
Integrable function 121
integral see Lebesgue Riemann Bochner Pettis
Interior 30
Intermediate Value Theorem 43
Intersection 5—7 507
Interval topology 42
Intervals 24—25
Into (function) 5
Invariant: means 274
Invariant: metric 71
Invariant: set 267 374
Inverse: image 27
Inverse: relation 9 508
Ionescu Tulcea, C. 275
Isolated point 48
Isometry 58 169
Isonormal process 444 481 532—533
Iterated integrals 134—142 343—344
Iterated logarithm 476—480 482—483
Ito, K. 481
Jacobs, K. 277
Jech, T. 22 527
Jensen inequality 348—349 381
Jensen, J.L.W.V. 219 381
Jessen, B. 275 331 332 480
Jointly measurable 139
Jointly normal 312 315
Jordan decomposition 179
Jordan, Camille 111 184—185 246
Jordan, Karoly 274
Kac, M. 482
Kahane, J.-P. 481
Kakutani, S. 246 275 277 481 540
Kantorovich, L.V. 435
Kelley, J.L. 48 77 79 218 518
Kesten, H. 379 483
Khinchin, A. 276 277 330 332 482 500
Kiefer, J. 482
Kingman, J.F.C. 382
Kirszbraun, M.D. 218
Kisynski, J. 76
Klass, M.J. 483
Kleene, S.C. 503 505 518
Kodaira, K. 246
Koenig, D. 434
Kolmogorov — Smirnov statistics 460 482
Kolmogorov, A.N. 77 112 246 273—276 332 381 480 482 500
Kolmogorov: existence theorem for stochastic processes 441—443 480 531
Kolmogorov: inequality 323
Kolmogorov: zero-one law 270
Koopmans, T.C. 435
Korolyuk, V.S. 332
Korselt, A. 22
Kostka, D.G. 482
Krivine, J.-L. 519
Kronecker, L. 332
Kuiper, N.H. 482
Kunze, R. 308
Kuratowski, K. 76 78 148 500 518 527
Ky Fan 330
L-, L*-convergence 33
Lacroix, S.F. 247
Lagrange, J. 247
Lamb, C.W. 382
Landau, E. 519
Laplace, P.S. de 247 330—331 433 481
Lattice of functions 142
Lattice of sets 99
Lattice-indexed variables 379
Laws (of random variables) 282—283
Laws (of random variables), convergence 291—297 304—307 330 385—438
Laws of large numbers 260—266
Laws of the iterated logarithm 476—480 482—483
Le Cam, L. 275 434
Lebesgue, H. 76 79 80 85 112 148—149 185 246 330 500
Lebesgue: decomposition 175 179
Lebesgue: differentiation theorems 228—235
Lebesgue: dominated convergence theorem 132 149
Lebesgue: integral 114 120 148
Lebesgue: measurable function 123
Lebesgue: measure 98 105—109
Lebesgue: measure on  139—142 149
Ledrappier, F. 379
Legendre polynomials 172
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