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Bogachev V.I. — Measure Theory Vol.1
Bogachev V.I. — Measure Theory Vol.1

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Название: Measure Theory Vol.1

Автор: Bogachev V.I.

Аннотация:

Measure theory is a classical area of mathematics born more than two thousand years ago. Nowadays it continues intensive development and has fruitful connections with most other fields of mathematics as well as important applications in physics.

This book gives an exposition of the foundations of modern measure theory and offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course (the material of this level corresponds to a variety of special courses), and, finally, more specialized topics partly covered by more than 850 exercises.

Volume 1 (Chapters 1-5) is devoted to the classical theory of measure and integral. Whereas the first volume presents the ideas that go back mainly to Lebesgue, the second volume (Chapters 6-10) is to a large extent the result of the later development up to the recent years. The central subjects in Volume 2 are: transformations of measures, conditional measures, and weak convergence of measures. These three topics are closely interwoven and form the heart of modern measure theory.

The organization of the book does not require systematic reading from beginning to end; in particular, almost all sections in the supplements are independent of each other and are directly linked only to specific sections of the main part.

The target readership includes graduate students interested in deeper knowledge of measure theory, instructors of courses in measure and integration theory, and researchers in all fields of mathematics. The book may serve as a source for many advanced courses or as a reference.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 500

Добавлена в каталог: 22.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$A_n\downarrow A$      1
$A_n\uparrow A$      1
$A_X$      183
$BMO(\mathbb{R}^n)$      373 374
$C_0^{\infty}(\mathbb{R}^n)$      252
$d\nu/d\mu$      178
$f*g$      205
$f*\mu$      208
$f\dot\mu$      178
$f\sim g$      139
$f^{-1}(\mathcal{A})$      6
$H(\mu,\nu)      300
$H^s$      216
$H^s_{\delta}$      215
$H_{\alpha}(\mu,\nu)$      300
$int_Xf(x) \mu(dx)$      118
$I_A$      105
$L^0(\mu)$      139
$l^1$      281
$L^1(X,\mu)$      120 139
$L^1(\mu)$      120 139
$L^p(E)$      139 250
$L^p(X,\mu)$      139
$L^p(\mu)$      139 250
$L^{\infty}(\mu)$      250
$L^{\infty}_{loc}(\mu)$      312
$S(\mathcal{E})$      36
$W^{p,1}(\mathbb{R}^n, \mathbb{R}^k)$      379
$W^{p,1}(\Omega)$      377
$W^{p,1}_{loc}(\mathbb{R}^n, \mathbb{R}^k)$      379
$x\vee y$      277
$x\wedge y$      277
$X^+$      176
$X^-$      176
$\bar{f}$      200
$\delta$-ring of sets      8
$\delta_{\alpha}$      11
$\hat{f}$      197
$\int f(x)dx$      120
$\int_A f(x)(dx)$      116 120
$\int_Af d\mu$      116 120
$\lambda_n$      14 21 24 25
$\lim\inf\limit_{n\rightarrow\infty}E_n$      89
$\lim\sup\limit_{n\rightarrow\infty}E_n$      89
$\mathbb{N}^{\infty}$      35
$\mathbb{R}^n$      1
$\mathbb{R}^{\infty}$      143
$\mathcal{A}/\mu$      53
$\mathcal{A}_1\bar{\bigotimes}\mathcal{A}_2$      180
$\mathcal{A}_1\bigotimes\mathcal{A}_2$      180
$\mathcal{A}_{\mu}$      17
$\mathcal{B}(E)$      6
$\mathcal{B}(\mathbb{R}^n)$      6
$\mathcal{B}(\mathbb{R}^{\infty})$      143
$\mathcal{B}_A$      8 56
$\mathcal{E}$-analytic set      36
$\mathcal{E}$-Souslin set      36
$\mathcal{L}^0(X,\mu)$      139
$\mathcal{L}^0(\mu)$      108 139 277
$\mathcal{L}^1(\mu)$      118 139
$\mathcal{L}^p(E)$      139
$\mathcal{L}^p(X,\mu)$      139
$\mathcal{L}^p(\mu)$      139
$\mathcal{L}^{\infty}(\mu)$      250
$\mathcal{L}_N$      26
$\mathcal{M}(X, \mathcal{A})$      273
$\mathfrak{M}_m$      41
$\mu *$      16
$\mu$-a.e.      110
$\mu$-almost everywhere      110
$\mu$-measurab1e function      108
$\mu$-measurab1e set      17 21
$\mu$-measurability      17
$\mu*\nu$      207
$\mu\circ f^{-1}$      190
$\mu\sim\nu$      178
$\mu^+$,      176
$\mu^-$      176
$\mu_*$      57
$\mu_1\otimes\mu_2$      180 181
$\mu_1\times\mu_2$      180
$\mu_A$      23 57
$\mu|_A$      23 57
$\nu\ll\mu$      178
$\nu\perp\mu$      178
$\omega(\kappa)$      63
$\omega_0$      63
$\omega_1$      63
$\sigma$-additive class      33
$\sigma$-additive measure      10
$\sigma$-additivity      10
$\sigma$-algebra      4
$\sigma$-algebra, Borel      6
$\sigma$-algebra, complete with respect to $\mu$      22
$\sigma$-algebra, countably generated      91
$\sigma$-algebra, generated by functions      143
$\sigma$-algebra, generated by sets      4
$\sigma$-complete structure      277
$\sigma$-hnite measure      24 125
$\sigma$-ring of sets      8
$\sigma$theorem      239
$\sigma(E, F)$      281
$\sigma(\mathcal{F})$      4 143
$\tau*$      43
$\tau_*$      70
$\tilde{\mu}$      197
$\vee F$      277
$\|f\|_p$      140
$\|f\|_{L^p(\mu)$      140
$\|f\|_{\infty}$      250
$\|\mu\|$      176
$|\mu|$      176
A + B      40
A + h      27
A-operation      36 420
a.e.      110
Aaplim      369
Absolute continuity of Lebesgue integral      124
Absolute continuity of measures      178
Absolute continuity, uniform of integrals      267
Absolutely continuous function      337
Absolutely continuous measure      178
Abstract inner measure      70
AC[a, b]      337
Adams M.      413
Adams R.A.      379
Additive extension of a measure      81
Additive set function      9 218 302
Additivity, countable      9
Additivity, finite      9 303
Airault H.      414
Akcoglu M.      435
Akhiezer (Achieser) N.I.      247 261 305
Akilov G.P.      413
Alaoglu L.      283
Alekhno E.A.      157 434
Aleksandrova D.E.      382
Aleksjuk V.N.      293 423 433
Alexander R.      66
Alexandroff (Aleksandrov) A.D.      vii viii 237 409 417 422 429 431
Alexandroff P.S.      411 420 437
Algebra of functions      147
Algebra of sets      3
Algebra, Boolean metric      53
Algebra, generated by sets      4
Aliprantis Ch.D.      413 415
Almost everywhere      110
Almost uniform convergence      111
Almost weak convergence in L      280
Alt H.W.      413
Amarm H.      413
Ambrosia L.      379
Amerio L.      414
Analytic set      36
Anderson inequality      225
Anderson T.W.      225
Anger B.      413 415
Ansel J.-P.      415
Antosik P.      319
Approximate continuity      369
Approximate derivative      373
Approximate differentiability      373
Approximate limit      360
Approximating class      13 14 15
Areshkin (Areskin) G.Ya.      293 321 322 418 433
Arias de Revna J.      260
Arino O.      415
Arnaudies J.-M.      413
Arora S.      414
Artemiadis N.K.      413
Ascherl A.      59
Ash R.B.      413
Asplund E.      413
atom      55
Atomic measure      55
Atomless measure      55
Aurnann G.      411 413
Axiom, determinacy      80
Axiom, Martin      78
B(X, A)      291
Bahvalov A.N.      415
Baire R.      88 148 166 409
Baire, category theorem      80
Baire, class      148
Baire, theorem      166
Ball J.M.      316
Banach H.      61 67 81 170 171 249 264 283 388 392 406 409 417 419 422 424 430 433 438
Banach Saks property      285
Banach space      240
Banach space, reflexive      281
Banach — Alaoglu theorem      283
Banach — Steinhaus theorem      264
Banach — Tarski theorem      81
Barra .l.-R.      412 434
Barra G. de      413
Bartle R.G.      413 437
Bary N.K.      85 261 392 407
Basis, Hamel      65 86
Basis, orthonormal      258
Basis, Schauder      296
Bass J.      413
Basu A.K.      413
Bauer H.      v 309 413
Beals R.      414
Bear H.S.      413
Behrends E.      413
Belkner H.      413
Bellach J.      413
Bellow A.      435
Benedetto J.J.      160 413 415 436
Benoist J.      415
Beppo Levi Theorem      130
Berberian S.K.      413
Berezansky Yu.M.      413
Bergh J.      435
Bernstein F.      63
Bernstein set      63
Bertin E.M.J.      431
Besicovitch A.S.      65 314 361 421 435 436
Besicovitch, ample      66
Besicovitch, set      66
Besicovitch, theorem      361
Besov O.V.      379
Bessel inequality      259
Bessel W.      259
Bichteler K.      413 423
Bienayme J.      428
Bierlein D.      59 421
Billingsley P.      413
Bingham N.H.      412 416
Birkhoff G.      421
Birkhoff G.D.      viii
Bishop E.      423
Bliss G.A.      410
Blumberg H.      421
Bobkov S.G.      431
Bobynin M.N.      324
Boccara N.      413
Bochner S.      220 430
Bochner theorem      220
Bogachev V.I.      198 382 408 411 420 431
Bogoliouboff (Bogolubov, Bogoljubov) N.N.      viii
Bogoljubov (Bogolubov) A.N.      416
Boman J.      228
Boolean algebra metric      53
Borel $\sigma$-algebra      6
Borel E.      v vii 6 90 106 409 410 416 417 427 430
Borel function      106
Borel mapping      106 145
Borel measure      10
Borel set      6
Borel — Cantelli lemma      90
Borell C.      226 431
Borovkov A.A.      413
Botts T.A.      414
Bouaiad A.      413
Bounded mean oscillation      373
Bourbaki N.      412
Bourgain J.      316
Bouyssel M.      415
Brascamp H.      431
Brehmer S.      413
Brenier Y.      382
Brezis H.      248 298
Briane M.      413
Bridges D.S.      414
Brodskii M.L.      235 408
Brooks J.K.      434
Broughton A.      84
Browder A.      414
Brown A.B.      84
Bruckner A.M.      210 332 395 401 402 413 421 436 438
Bruckner J. B.      210 413 421 436 438
Brudno A.L.      414
Brunn H.      225
Brunn — Minkowski inequality      225
Brunt B. van      425
Brzuchowski J.      421
Buchwalter H.      413
Buczolich Z.      172
Buistin C.      400
Bukovsky L.      421
Buldygin V.V.      80 431
Bungart L.      413
Bunyakowsky (Bunyakovskii, Bounjakowskv) V.Ja.      141 428
Burago D.M.      227 379 431
Burenkov V.I.      391
Burk F.      413
Burkill J.C.      410 413 423 437
Burkinshaw O.      413 415
Burrill C.W.      413
Buseman H.      215 437
BV($\Omega$)      378
BV[a, b]      333
Caccioppoli R.      378 433
Caccioppolli set      378
Caffarelli L.      382
Cafiero F.      413 415 433
Calbrix J.      413
Calderon A.P.      385 436
1 2 3 4 5 6 7
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