Dudley R.M., Fulton W. (Ed) — Real Analysis and Probability :: Электронная библиотека попечительского совета мехмата МГУ

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Dudley R.M., Fulton W. (Ed) — Real Analysis and Probability

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Название: Real Analysis and Probability

Авторы: Dudley R.M., Fulton W. (Ed)

Аннотация:

This is a reissue of textbook covering graduate level courses in probability theory and real analysis, each conceived as a one-semester course. Dudley (Massachusetts Institute of Technology), in an effort to make the text self-contained, has added a treatment of the Stone- Weierstrass theorem

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 2002

Количество страниц: 566

Добавлена в каталог: 11.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

-bounded      355
spaces      153 158 208—211
$\sigma$ -algebra      86 97 99
$\sigma$ -compact      226
$\sigma$ -finite measure      91
$\sigma$ -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 $\mathbb{R}^k$       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, $\sigma$ -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, $\sigma$ -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 $\emptyset$       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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