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Dudley R.M., Fulton W. (Ed) — Real Analysis and Probability |
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Ïðåäìåòíûé óêàçàòåëü |
-bounded 355
spaces 153 158 208—211
-algebra 86 97 99
-compact 226
-finite measure 91
-rings 105 118
a.e. 130
a.s. 260—261
Abel, N.H. 77
Abelian group 70—71
Absolutely continuous functions 233—235
Absolutely continuous measures 174 235
Acosta, A. de 435 483
Adapted 358
Additivity of integrals 120—121
Affine group of the line 71
Affine transformation on 311
Aganbegyan, A.G. 435
Ahlfors, L.V. 523—525
Akilov, G.P. 435
Alaoglu's theorem 194
Alexandroff, A.D. 330 433
Alexandroff, P.S. 76—80 332 433 500
Alexits, G. von 148
Algebra, -algebra 86 97 99 115
Almost: everywhere 130
Almost: invariant 273
Almost: sure convergence 287—291
Almost: surely 260—261
Almost: uniform convergence 243—244
Ambrose, W. 246
Analytic functions 523
Analytic sets 493—500
Ancestor 17
Andersen, E.S. 275 381 382 480
Andre, D. 482
antisymmetric 10
Arboleda, L.C. 76
Archibald, R.C. 331
Area 139—140
Arithmetic-geometric means 156 352
Arkhangelskii, A.V. 77 79
Arzela — Ascoli theorem 52 78
Arzela, C. 78
Ascoli, G. 78
Associative 69
Asymptotic 477
Atom: of a measure 109
Atom: of an algebra 115
Axiom of Choice 18—22 514 518
Axiomatic set theory 503—520
Babylonia 183
Bachelier, L. 480 482
Baez-Duarte, L. 382
Baire category theorem 79 277
Baire property 245
Baire sets 222—227 235—238
Baire, R. 78 79 277
Ball 26
Ballot problem 482
Banach space 158 183 219
Banach, S. 183 218—219 274 527
Bar-Hillel, Y. 519
Bari, N. 500
Baron, M.E. 331
Barone, J. 273 276
Bartle, R.G. 78 219
Base: filter 29
Base: neighborhood 26
Base: of a topology 26
Base: of a uniformity 68
Basis: of a Banach space 169
Basis: orthonormal 165—173
Bauer, H. 382
Bell, W.C. 184
Benzi, M. 276
Bernays, P. 517
Bernoulli, Jakob 276 330 331
Bernstein, F. 22
Bernstein, S.N. 332
Bessel inequality 167
Bessel, F.W. 184
beta function 286—287
Bicompact 76
Bienayme, J. 275—276
Biermann, K.-R. 78
Bilateral shift 271
Billingsley, P. 277
Bingham, N.H. 273 483
Binomial probabilities 254 287 300—301 303 318 432
Birkhoff, G.D. 276 277 382
Bishop, E. 518
Blackwell, D. 381
Bledsoe, W.W. 149 533 540
Blood groups 22
Blumenthal, R.M. 539
Bochner integral 194—195
Bochner, S. 332 480
Boltzmann, L. 276—277
Bolzano, B. 75—76
Bonferroni inequality 265
Bonnesen, T. 218
Boorman, K.E. 22
Borel isomorphism 487—493 500
Borel paradox 350—351
Borel sets, -algebra 98 119 123 129 130 222—228 235—239 487
Borel — Cantelli lemma 262
Borel, E. 22 76 85 111 273 276
Borsuk, K. 79
Bound variable (logic) 505
Boundary 32 386
Bounded: above (set) 8 516
Bounded: function 34 155
Bounded: variation 184 230—234
Bourbaki, N. 76 79 530
Bray, H.E. 433
Breiman, L. 326 482
Browder, F. 481
Brown, Robert 480
Brownian bridge 445—446 460—469
Brownian bridge from Brownian motion 446 461
Brownian bridge, definition 445
Brownian bridge, law of maximum 462
Brownian bridge, law of maximum modulus 464
Brownian bridge, law of sup and inf 465
Brownian motion 444—476
Brownian motion from isonormal process 447
Brownian motion, continuity of paths 446—448
Brownian motion, definition 445
Brownian motion, distribution of maximum 459
Brownian motion, lines, hitting 468
Brownian motion, log log law 477
Brownian motion, strong Markov property 450—458
Brownian motion, tied down, pinned 461
Brownian motion, with filtration 453
Brunel, A. 277
Brunn — Minkowski inequality 216—218
Brunn, H. 218
Brush, S.G. 277
Buck, R.C. 183
Buffon, G. 274
Bunyakovsky, V.Y. 182
Burali — Forti paradox 514
CA set 500
Cantelli, F.P. 276 434
Cantor function 124 178 232
Cantor set 106 124 490
Cantor, G. 22 75
Caratheodory, C. 76 79 111
Cardinality, cardinals 16—17 514—515
| Carleson, L. 246
Cartan, H. 76 274
Cartesian product 8 38—39 508
Cartesian product for measures 134—142 255—260
Cartesian product, infinite 38—39 50 62 255—260
Category theorem 59
Category theory 518
Cauchy, A.-L. 75 77—78 149 182
Cauchy: distribution 324 328
Cauchy: inequality 154 162 182
Cauchy: net 70
Cauchy: sequence 44
Cech, E. 74 76—77 79—80
Central limit theorems 282 306—307 315—319 330—332
Chacon, R.V. 277
Chain 19
Change of variables in integrals 121
Characteristic function (Fourier transform) 298—310 331—332
Characteristic function (Fourier transform), derivatives of 301
Characteristic function (Fourier transform), infinitely divisible 327
Characteristic function (Fourier transform), inversion 303—305
Characteristic function (Fourier transform), multiplication 301
Characteristic function (Fourier transform), multivariate normal 306—308
Characteristic function (Fourier transform), normal (univariate) 300
Characteristic function (Fourier transform), Poisson 327
Characteristic function (Fourier transform), stable 328
Characteristic function (Fourier transform), uniqueness 303—305 314
Charge, electric 178
Chebyshev's inequality 261 275—276
Chebyshev, P.L. 275
Chi-squared 315
Chittenden, E.W. 79
Choice, axiom of 18—22 514 518
Chord 203
Chung, K.L. 276
Church, A. 505
Class, proper 517—518
Closed graph theorem 213
Closed interval 24 35
Closed interval, regular set, measure 224
Closed interval, set 25
Closure 30—31
Cohen, P. 505 518
Cohn, D. 500
Cohn, Harry 276
coin tossing 250
Collection 25
Compact linear operator 215
Compact sets and spaces 34—42
Compact sets and spaces, metric spaces 44—48
Compact sets and spaces, nonmetric spaces, pathology 530—540
Compactification 71—74 530
Complement 25
Complete metric space 44 58
Complete uniform space 70
Completely regular 73 79
Completeness of 158—159
Completion: inner product space 171
Completion: metric space 58
Completion: of a measure 101—105
Complex conjugate 160 521
complex numbers 153 521—524
Composition of functions 39—40
Conditional distributions 342—347 350 413
Conditional expectations 336—341 381
Conditional expectations, Fatou's lemma 340
Conditional expectations, Jensen's inequality 349
Conditional probability 336 364
Conditional probability, regular 341 351 381
Cone 195
Connected set 43 492
Consistent laws (stochastic process) 440
Consistent sequence of estimators 426
CONTAINS 3
Contingency tables 429
Continuity sets 386 388
continuous 28
Continuous at 86
Continuous from the right 87 232 283
Continuous in probability (stochastic process) 445
Continuous, mapping theorem 296
Continuum 17
Continuum Hypothesis 17 487 515 518
Contraction 268 277
Convergence 24 27—29
Convergence for nets 29
Convergence in measure 133 330
Convergence in probability 261 287—291 295
Convergence in total variation 292
Convergence metrization 393—399 404—413 434—435
Convergence of distribution functions 295—296 307 387 398 425
convergence of integrals 130—134
Convergence of laws 291—297 304—307 330 385—438
Convergence, almost surely 261 287—291
Convergence, almost uniformly 243—244
Convergence, pointwise 24 42
Convergence, sequential (L-) 33
Convex: combination 195 199
Convex: functions 203—208 219 329 347—349 351—352 381
Convex: sets 164 195—203 216—219 352
Convolution 284 303—304 310 314 326
Coordinate projections, spaces 38
Corners, Quine's 504 518
Correlation (coefficient) 255
cosets 108
Countable 16
Countably additive 85 178—181 343 346 362
Counting measure 87 122
Courant, R. 525
Covariance 253 306 445
Covariance matrix 306—308
Cover, covering 34
Cramer, H. 332
Cumulative distribution function 283
Cuts, Dedekind 7—8 516—517
Dall Agllo, G. 435
Daniell integral 142—148 274—275
Daniell, P.J. 149 184 274—275
Daw, R.H. 331
Day, M.M. 274
de Moivre, A. 330—331 433
Decimal expansions 44—45 517
Decomposition of submartingales 354 373
Dedekind, R. 516 518
Definitions, formal and informal 1—2
Dellacherie, C. 500
Dense 31
Dense in itself 490
Dense, nowhere 59
Density points 534
Density, of a measure 177 284 298
derivatives 228—232
Derivatives of characteristic functions 301
Derivatives, left and right 204—205
Derivatives, Radon — Nikodym 177
Derived set 75
Determinant 315
Determining classes 99 259
Diaconis, P. 434
Diagonal 10
Diameter 47
Die, dice 251 273
Dieudonne, J. 218 381
Differentiation of integrals 133 228
Dini's theorem 53 78
Dini, U. 78
Direct sum of measure spaces 141
Directed set 28
Directional derivatives 205
Discrete topology 25
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