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Bogachev V.I. — Measure Theory Vol.2
Bogachev V.I. — Measure Theory Vol.2

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Название: Measure Theory Vol.2

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

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Предметный указатель
$A_{n}\downarrow A$      I: 1
$A_{n}\uparrow A$      I: 1
$a_{x}$      I: 183
$B(X,\mathcal{A})$      I: 291
$BMO(\mathbb{R}^{n})$      I: 373 374
$BV(\Omega)$      I: 378
$C_{0}^{\propto}(\mathbb{R}^{n})$      I: 252
$C_{b}(X)$      II: 3
$d\nu/d\mu$      I: 178
$f\ast g$      I: 205
$f\ast\mu$      I: 208
$f\cdot\mu$      I: 178
$f\sim g$      I: 139
$f^{-1}(\mathcal{A})$      I: 6
$F_{\sigma}$-set      II: 7
$f|_{A}$      I: 1
$H(\mu,\nu)$      I: 300
$H^{s}$      I: 216
$H^{s}_{\delta}$      I: 215
$H_{\alpha}(\mu,\nu)$      I: 300
$I_{A}$      I: 105
$k_{R}$-space      II: 56 220
$Lip_{1}(X)$      II: 191
$L^{0}(\mu)$      I: 139
$l^{1}$      I: 281
$L^{1}(X,\mu)$      I: 120 139
$L^{1}(\mu)$      I: 120 139
$L^{p}(E)$      I: 139 250
$L^{p}(X,\mu)$      I: 139
$L^{p}(\mu)$      I: 139 250
$L^{\propto}(\mu)$      I: 250
$L^{\propto}_{loc}(\mu)$      I: 312
$S(\mathcal{E})$      I: 36; II: 49
$V_{a}^{b}(f)$      I: 332
$W^{p,1}(\mathbb{R}^{n},\mathbb{R}^{k})$      I: 379
$W^{p,1}(\Omega)$      I: 377
$W^{p,1}_{loc}(\mathbb{R}^{n},\mathbb{R}^{k})$      I: 379
$x\vee o$      I: 277
$x\wedge o$      I: 277
$x^{+}$      I: 176
$x^{-}$      I: 176
$\aleph$-compact measure      II: 91
$\beta X$      II: 5
$\beta(X,X^{\ast})$      II: 124
$\check{f}$      I: 200
$\delta$-ring of sets      I: 8
$\delta_{a}$      I: 11
$\frac{\liminf}{n\rightarrow\propto} E_{n}$      I: 89
$\frac{\limsup}{n\rightarrow\propto} E_{n}$      I: 89
$\int_{A}f d\mu$      I: 116 120
$\int_{A}f(x)dx$      I: 120
$\int_{A}f(x)\mu(dx)$      I: 116 120
$\int_{X}f(x)\mu(dx)$      I: 118
$\lambda_{n}$      I: 14 21 24 25
$\mathbb{E}(f|\mathcal{B})$      II: 340
$\mathbb{E}(\xi|\eta)$      II: 340
$\mathbb{E}f$      II: 340
$\mathbb{E}^{\mathcal{B}}$      II: 340
$\mathbb{E}^{\mathcal{B}}_{\mu}$      II: 340
$\mathbb{N}^{\propto}$      I: 35; II: 6
$\mathbb{R}^{n}$      I: 1
$\mathbb{R}^{\propto}$      I: 143; II: 5
$\mathcal{A}/\mu$      I: 53
$\mathcal{A}_{1}\otimes {\mathcal{A}}_{2}$      I: 180
$\mathcal{A}_{1}\overline{\otimes} \mathcal{A}_{2}$      I: 180
$\mathcal{A}_{\mu}$      I: 17
$\mathcal{B}(E)$      I: 6
$\mathcal{B}(\mathbb{R}^{n})$      I: 6
$\mathcal{B}(\mathbb{R}^{\propto})$      I: 143
$\mathcal{B}a(X)$      II: 12
$\mathcal{B}_{A}$      I: 8 56
$\mathcal{B}{X)$      II: 10
$\mathcal{D}'(\mathbb{R}^{d})$      II: 55
$\mathcal{D}(\mathbb{R}^{d})$      II: 55
$\mathcal{E}$-analytic set      I: 36; II: 46
$\mathcal{E}$-Souslin set      I: 36; II: 46
$\mathcal{F}$-analytic set      II: 49
$\mathcal{F}$-Souslin set      II: 49
$\mathcal{K}$-analytic set      II: 49
$\mathcal{L}^{0}(X,\mu)$      I: 139
$\mathcal{L}^{0}(\mu)$      I: 108 139 277
$\mathcal{L}^{1}(\mu)$      I: 118 139
$\mathcal{L}^{p}(E)$      I: 139
$\mathcal{L}^{p}(X,\mu)$      I: 139
$\mathcal{L}^{p}(\mu)$      I: 139
$\mathcal{L}^{\propto}(X,\mu)$      I: 250
$\mathcal{L}_{n}$      I: 26
$\mathcal{M}(X,\mathcal{A})$      I: 273
$\mathcal{M}_{r}(X)$      II: 77
$\mathcal{M}_{r}^{+}(X)$      II: 77
$\mathcal{M}_{t}(X)$      II: 77
$\mathcal{M}_{t}^{+}(X)$      II: 77
$\mathcal{M}_{\sigma}(X)$      II: 77
$\mathcal{M}_{\sigma}^{+}(X)$      II: 77
$\mathcal{M}_{\tau}(X)$      II: 77
$\mathcal{M}_{\tau}^{+}(X)$      II: 77
$\mathcal{P}_{r}(X)$      II: 77
$\mathcal{P}_{t}(X)$      II: 77
$\mathcal{P}_{\sigma}(X)$      II: 77
$\mathcal{P}_{\tau}(X)$      II: 77
$\mathcal{S}(X)$      II: 21
$\mathcal{T}(X^{\ast},X)$      II: 124
$\mathfrak{M}_{\mathfrak{m}}$      I:41
$\mid\mu\mid$      I: 176
$\mu$-a.e.      I: 110
$\mu$-almost everywhere      I: 110
$\mu$-measurability      I: 17
$\mu(A|x)$      II: 357
$\mu(A|\mathcal{B})$      II: 345
$\mu(A|\xi)$      II: 345
$\mu\alpha\Rightarrow\mu$      II: 175
$\mu\ast f^{-1}$      I: 190; II: 267
$\mu\ast\nu$      I: 207
$\mu\sim\nu$      I: 178
$\mu^{+}$      I: 176
$\mu^{x}$      II: 357
$\mu^{y}_{\mathcal{A}_{0}}$      II: 358
$\mu^{\ast}$      I: 16
$\mu^{\mathcal{B}}$      II: 345
$\mu^{\mathcal{B}}(A|x)$      II: 357
$\mu^{\mathcal{B}}_{\mathcal{A}_{0}}(A,x)$      II: 358
$\mu_{-}$      I: 176
$\mu_{1}\otimes\mu_{2}$      I: 180 181
$\mu_{1}\times\mu_{2}$      I: 180
$\mu_{A}$      I: 23 57
$\mu_{\ast}$      I: 57
$\mu|_{A}$      I: 23 57
$\nu\ll\mu$      I: 178
$\nu\perp\mu$      I: 178
$\omega(\kappa)$      I: 63
$\omega_{0}$      I: 63
$\omega_{1}$      I: 63
$\parallel f\parallel_{L^{p}(\mu)}$      I: 140
$\parallel f\parallel_{p}$      I: 140
$\parallel f\parallel_{\propto}$      I: 250
$\parallel\mu\parallel$      I: 176
$\sigma$-additive, class      I: 33
$\sigma$-additive, measure      I: 10
$\sigma$-additivity      I: 10
$\sigma$-algebra      I: 4
$\sigma$-algebra, asymptotic      II: 407
$\sigma$-algebra, Baire      II: 12
$\sigma$-algebra, Borel      I: 6; II: 10
$\sigma$-algebra, complete with respect to /i      I: 22
$\sigma$-algebra, countably generated      I: 91; II: 16
$\sigma$-algebra, countably separated      II: 16
$\sigma$-algebra, generated by functions      I: 143
$\sigma$-algebra, separahle      II: 16
$\sigma$-algebra, tail      II: 407
$\sigma$-compact space      II: 5
$\sigma$-complete structure      I: 277
$\sigma$-finite measure      I: 24 125
$\sigma$-homomorphism Boolean      II: 321
$\sigma$-ring of sets      I: 8
$\sigma(E,F)$      I: 281
$\sigma(\mathcal{F})$      I: 4 143
$\tau$-additive measure      II: 73
$\tau^{\ast}$      I: 43
$\tau_{0}$-additive measure      II: 73
$\tau_{\ast}$      I: 70
$\vee F$      I: 277
$\widehat{f}$      I: 197
$\widetilde{\mu}$      I: 209
A+h      I: 27
A-operation      I: 36 420
a.e.      I: 110
Absolute continuity of Lebesgue integral      I: 124
Absolute continuity of measures      I; 178
Absolute continuity, uniform of integrals      I: 267
Absolutely continuous function      I: 337
Absolutely continuous measure      I: 178
Abstract inner measure      I: 70
Acosta A. de.      II: 451
AC[a,b]      I: 337
Adamaki W.      II: 131 156 244 336 444 450 451 456 462
Adams M.      I: 413
Adams R.A.      I: 379
Additive extension of a measure      I: 81
Additive set function      I: 9 218 302
Additivity, countable      I: 9
Additivity, finite      I: 9 303
Afanas’eva. L.G.      II: 440
Airault H.      I: 414
Akcoghi M.      I: 435
Akhlezer (Achleser) N.I.      I: 247 261 305
Akilov G.P.      I: 413; II: 453
Akin E.      II: 288
Alaoglu L.      I: 283
Aldaz J.M.      II: 131 166 450
Aldous D.J.      II: 409 464
Alekhno E.A.      I: 157 434
Aleksandrova D.E.      I: 382; II: 418 424
Aleksjuk V.N.      I: 293 423 433
Alexander R.      I: 6ft
Alexandroff (Aleksandrov) A.D.      I: vii viii. 409 417 422 431 429; 108 113 135 179 184 250 442 443 447 451 452 453 454
Alexandroff A.D. theorem      II: 184
Alexandroff P.H.      I: 411 420 437; 9 439
Alfsen E.M.      II: 146
Algebra, boolean      II: 326
Algebra, Boolean metric      I: 53
Algebra, generated by sets      I: 4
Algebra, of functions      I: 147
Algebra, of seta      I: 3
Aliprantis Ch.D.      I: 413 415
Almost everywhere      I: 110
Almost homeomorphisim of measure spaces      II: 286
Almost Lindeloef space      II; 1.41
Almost uniform convergence      I; 111
Almost weak convergence in L1      I: 289
Alpern S.      II: 288 459
Alt H.W.      I: 413
Alternative, Fremlin      II: 153
Alternative, Kakutani      II: 351
Amann H.      I: 413
Ambrose W.      II: 448
Ambrosio L.      I: 379; 236 454 460
Amemiya I.      II: 156 443
Amerio L.      I: 414
Analytic set      I: 36; II: 20 46
Andersen E.S.      II: 461
Anderson inequality      I: 225
Anderson T.W.      I: 225
Anger B.      I: 413 415; 451
Aniszczyk B.      II: 173
Anosov D.V.      II: 335
Ansel J.-P.      I: 415
Antosik P.      I: 319
aplim      I: 369
Approximate continuity      I: 369
Approximate derivative      I: 373
Approximate differentiability      I: 373
Approximate limit      I: 369
Approximating class      I: 13 14 15
Areshkin (Areskin) G.Ya.      I: 293 321 322 418 433
Argyros S.      II: 450
Arias de Reyna J.      I: 260
Arino O.      I: 415
Arkhangel’skii A.V.      II: 9 64
Armstrong T.      II: 451
Arnaudies J.-M.      I: 413
Arnold V.I.      II: 391
Arora S.      I: 414
Arsenin V.Ya.      II: 37 439 441
Artemiadis N.K.      I: 413
Ascherl A.      I: 59
Ash R.B.      I: 413
Asplund E.      I: 413
Asymptotic $\sigma$-algebra      II: 1117
atom      I: 55
Atomic measure      I: 55
Atomless measure      I: 55; II: 133 317
Aumann Ci.      I: 411 413
Aumann R.J.      II: 40
Automorphism of measure space      II: 275
Averna D.      II: 138
Avez A.      II: 391
Axiom, determinacy      I: 90
Axiom, Martin      I: 78
Ayerbe-Toledano J.-M.      II: 451
Babiker A.G.      II: 136 163 288 334 450 451
Bachman G.      II: 131 451
Bade W.G.      II: 456
Badrikiari A.      II: 447
Bahvalov A.N.      I: 415
Baire $\sigma$-algebra      II: 12
Baire category theorem      I: 89
Baire class      I: 148
Baire measure      II: 68
Baire R.      I: 88 148 166 409; 12 43ft
Baire set      II: 12
Baire theorem      I: 166
Baker R.      II: 335
Balder E.J.      II: 249
Ball J.M.      I: 316
Banach S.      I: 61 67 81 170 171 249 264 283 388 392 406 409 417 419 422 424 430 433 438; 440 446 458 460—464
Banach space      I: 249
Banach space, reflexive      I: 281
Banach — Alaoglu theorem      I; 283
Banach — Saks property      I: 285
Banach — Steinhaus theorem      I: 261
Banach — Tarcki theorem      I: 81
Banakh T.O.      II: 202 225 228 454 455 456
Barone J.      II: 464
Barra G. de      I: 413
Barra J.-R.      I: 412 434
Barrelled space      II: 123
Bartte R.G.      I: 413 437
Bary N.K.      I: 85 261 392 407
Baryrenter      II: 143
Base of topology      II: 1
Basil A.K.      I: 413
Basis of a measure space      II: 280
Basis, Hamel      I: 65 86
Basis, orthonormal      I: 258
Basis, Sell mi ? for      I: 296
Bass J.      I: 413
Bass R.F.      II: 461
Batt J.      II: 447
Bauer H.      I: v 309 413; 410 458 461
Baushev A.N.      II: 456
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