Bourgin R.D. — Geometric Aspects of Convex Sets with the Radon-Nikodym Property :: Электронная библиотека попечительского совета мехмата МГУ

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Bourgin R.D. — Geometric Aspects of Convex Sets with the Radon-Nikodym Property

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Название: Geometric Aspects of Convex Sets with the Radon-Nikodym Property

Автор: Bourgin R.D.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1983

Количество страниц: 492

Добавлена в каталог: 08.07.2008

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Предметный указатель

$G_{\delta}$ (dense)      44 45 55 56 70 117 131 160 161 329 401
$\mu$ -Completion of G      101
$\sigma$ -Isomorphism (between measurable spaces)      175
Almost separably valued      4 5
Almost surely (= almost everywhere)      4
Analytic set      180 181
Analytic, K-analytic      365 373
Analytic, weakly K-analytic      365 371 380
Asplund Property (AP)      116 117 120 121 131 133 136 138 141 144
Asplund spaces      116 117 132 136 137 141 150 156 157 163 169
Asplund, weak* Asplund Spaces      161
Average Range (of a vector measure)      2
Average Range (of a vector measure), locally s-dentable average range      23
Baire $\sigma$ -algebra      99
Baire category (first or second)      53 57 58
Baire category theorem      45 60
Baire class n      379
Baire functions      100
Banach — Mazur distance      249 250
Barycenter      178 182 183 204 205 216 218 225 239 306
Barycenter, barycentric calculus (or formula)      306 310 376
Biorthogonal system      96 97
Bishop — Phelps Property (BPP)      387 388
Bishop — Phelps Theorem 3.3.1      38 45 46 49 53 57 62 149 387 431
Bishop's Lemma 3.2.7      44 55 329
Bochner integrable      4 5
Bochner integral      2 3 298 301
Bochner, indefinite Bochner integral      300
Boolean algebra with unit      434
Borel $\sigma$ -algebra      73 99 112 114 180 215 226
Bounded Lipshitz functions (space of)      184
Bourgain — Phelps Theorem 3.5.4 (and 3.5.4(w*))      55 56 58 61 93 240 325 329 390 394 420
Branch      335 403 415 417
Branch point      403 404 415
Branch, eventually left turning branch      335
Bush ( $\varepsilon$ -bush)      31 34 227 233 314 317 318 323 331 332 402 404 410 415 416
Bush decomposition      332
Bush indices      227 318
Bush, approximate bush      314 317 318
Bush, asymptotic subbush      403 404 410 415
Bush, complemented bush      416 417
Bush, stage (of a bush)      33 227 317 406-410
Cantor set      86 227 233 402
Category      see "Baire"
Center of mass      178
Choquet Bishop-de Leeuw Theorem      173 217
Choquet order      174 192
Choquet Theorem 3.2.3      41 42 43 173
Compact extension property      259
Compact of type RN      172
Compact operator      see "Operator"
Compact Range Property (CRP)      304 305
Compact, $\mu$ -measure compact      362
Compact, Eberlein compact      215
Compact, measure compact      347 361 362
Compact, norm compact      23 143 172 185 259 290 300 301 302 306
Compact, norm compact convex      172
Compact, real compact      347 361 362
Compact, totally disconnected compact Hausdorff      434
Compact, weak compact      23 59 76 132 214 306 312 313 426
Compact, weak compact convex      59 60 217 311
Compact, weak Compact Extension Property      259
Compact, weak* compact      71 91 306 310
Compact, weak* compact convex      45 52 54 56 74 76 91 95 96 93 102 111 137 172 306 310 369 441
Compact, weakly compact operator      see "Operator"
Complementable, separably      304
Complemented      see "Bush"
Complete continuity, set of      309
Condensation point, $\eta$ -condensation point      80
Condensation point, weak* condensation point      81
Conditional expectation      5
Conditional expectation (scalar)      7
Conditional expectation (X-valued)      8
Cone      45 46 205
Cone, hereditary subcone      208
Cone, positive cone      423
Cone, well capped cone      421
Continuity, D-continuity of monotone operator      126 127 131 132
Continuity, points of continuity      310
Continuity, points of continuity of the identity      50 52 91
Core (of f)      311 312
D-Gradient      117
Decomposition Theorem for quasi-martingales 7.5.3      314 313 328 338 342 404 433
Decomposition, generalized dyadic decomposition      332
Decomposition, Riesz decomposition Lemma      see "Riesz"
Decomposition, standard dyadic decomposition      332
Density character      79
Dentable      18 27 29 52 53 388
Dentable, c-dentable      18 27 29 30 31
Dentable, s-dentable      18 27 420
Dentable, subset c-dentable      18 31
Dentable, subset dentable      13 30 31 420
Dentable, subset s-dentable      15 18 20 21 23 30 31 71
Dentable, subset weak* dentable      54 56 91
Dentable, weak* dentable      54 112 313
Denting point      50 341 420 427
Denting point, weak* denting point      159
Descendant      282
Difference sequence (associated with a martingale)      266
Differentiable bump function      148 150 152 153 158
Differentiable, continuously differentiable bump function      158 see "Gateaux"
Differentiable, D differentiable      117 124 127
diffuse      see "Measure"
Dilation order      174 192
Dilation, $\mu$ -dilation      192 201
Dini's theorem      426
Disintegration of measures      225
Disintegration of measures, strict disintegration of measures      226
Distribution (of $\mu$ by $\psi$ )      100 174
Domain (of monotone operator)      119
Dominated ({ $F_{n}$ : n = 1, 2, ...} is dominated by { $q_{n}$ : n = 1, 2, ...})      267
Dual space, separable      73 75 78 79
Duality      116 143 159 390
Dualoid      163 166 168
Dunford — Pettis Theorem 4.1.3      71 73 77 78 242
Dunford, integrable      299
Dunford, integral      3
Edgar order      174
Ekeland — Lebourg Theorem 5.6.2      150 154
Epigraph      117 391
Equimeasurable      143 171
Equivalent, (M)-equivalent to the usual $\ell_{1}$ basis      262 290
Equivalent, weakly equivalent functions      310 311 312
Expectation      5 7
Exposed points      40 420
Exposed points, strongly exposed points      40 44 53 55 56 58 60 159 314 329 420
Exposed points, weak* strongly exposed points      41 45 56 91 112 159
Extremal      90 402
Extreme point      17 39 40 41 50 61 67 74 181 204 214 215 225 306 331 341 345 414
Extreme point, $\varepsilon$ -strong extreme point      340 342
Extreme point, strong extreme point      340 341 345
Extreme point, strongly extreme point      67
Factorization (of operators)      132 135 309
Finite Tree Property (FTP)      34 243
Finitely representable      34
Flat      37
Frechet differentiable      117 150 151 156 157 161 167
Function version      318
Functional, exposing functional      40
Functional, strongly exposing functional      40 44 55 314 329
Functional, weak* strongly exposing functional      41 45 56
Gateaux differentiable      117
Gelfand — Frechet Property      16
General position      204
girth      36
GSG (Grothendieck — Stegall Generated) Spaces      172
GSP (Grothendieck — Stegall Property)      116 121 142 143 144 148 171 172 309
Haar system (of compact sets)      84
Hahn — Vitali — Saks Theorem 1.1.5      2 3 19 25 236
Helly's Theorem (Lemma 4.2.7)      83

Hereditary      436 437
Hilbert cube      44
Hilbert space      77 216
Identically distributed      268
Independence of a family of functions      268
Independence, axiomatic independence      101 300 301
Injective (Banach space)      147 258
Integrable, weak*      3 76
integral      see "Bochner" "Dunford" "Pettis"
Integral Representation Property (IRP)      224 225 238
Integral representations      173 201 418 420
Integral representations, uniqueness of integral representation      204 420
James Tree space JT      308
James, long James space J(to^)      346 347
K-analytic      see "Analytic"
Krein — Milman Property (KMP)      40 45 49 50 91 111 224 267 292 402 418 423
Krein — Milman Property (KMP), approximate Krein — Milman Property (AKMP)      42
Krein — Milman theorem      41 43 173
Lattice ordering      205
Lattice, Banach lattice      240 314 422 423 425
Levy's Theorem 1.3.1      8 19 27 73 78 146 178 209 237
Lifting      365 367
Lindelof      97 98 347 362 373
Lipschitz      see "Bounded" "Locally"
Locally $\varepsilon$ -supported      150
Locally bounded      119 124
Locally convex space      418
Locally Lipschitz      124
Lusin space      301 see
Martingale Convergence Property (MCP)      15 17
Martingale Convergence Property (MCP) for ( $\Omega$ ,F,P)      17 31
Martingale Convergence Property (MCP), elementary martingale convergence property      17 20 31
Martingale, $L^{1}$ -bounded martingale      12 25 33
Martingale, bounded martingale      11
Martingale, bush martingale      332 see
Martingale, dyadic martingale      265 266 332
Martingale, elementary martingale      11
Martingale, generalized dyadic martingale      332 342 345
Martingale, p-quasi-martingale      315 318
Martingale, quasi-martingale      314 315 323
Martingale, standard dyadic martingale      332 343 345
Martingale, submartingale      11
Martingale, X-valued martingale      11
Maximal inequality      9 10 25 27
Maximal, $<_{C}$ - maximal      see "Measure"
Maximal, $<_{D}$ maximal      see "Measure"
Maximal, $<_{E}$ maximal      see "Measure"
Maximal, $<_{SE}$ - maximal      176 181 387
Measurable in itself      171
Measurable space      1
Measurable, $F_{1}-F_{2}$ measurable function      100
Measurable, $\mu$ -Lusin measurable      364 368 369 376
Measurable, F-Borel measurable      4 5
Measurable, strongly F-measurable      4 5
Measurable, universally (Lusin) measurable      365 369 374
Measurable, universally measurable $\sigma$ -algebra U(B(D))      101 179
Measurable, universally measurable $\sigma$ -algebra with respect to tight measures $U_{t}(B(D))$       101 102 112 115
Measurable, universally weakly measurable      310
Measurable, weak* measurable      308
Measurable, weakly F-measurable      4 5
Measure, vector      2
Measure, vector, $<_{C}$ - maximal      201 204 205
Measure, vector, $<_{D}$ - maximal      201 204 205 387
Measure, vector, $<_{E}$ - maximal      201 204 205
Measure, vector, absolutely continuous with respect to P      2
Measure, vector, diffuse measure      219
Measure, vector, maximal measure      202
Measure, vector, of finite total variation      2
Measure, vector, probability measure      99
Measure, vector, Radon measure      99
Measure, vector, regular measure      99
Measure, vector, separable extremal measure      181 132 201 202 204 205 216 217 218 225 239
Measure, vector, separable measure space      383
Measure, vector, support of a measure      102 115
Measure, vector, tight measure      99 102 114
Measure, vector, variation of a vector measure      235 see
Michael's selection theorem      170
Milman Theorem 3.2.2      41 42 43 50 60 76 90 93 216
Modulus (of uniform convexity)      35
Moment problems      421
Monotone      see "Operator"
Movable ( $\mu$ -movable)      201
Neighborly Bush Property (NBP)      247
Neighborly Tree Property (NTP)      244 247
Norm      see "Uniformly" "Square"
Norming space      440
Operator, compact operator      145 259 260
Operator, Dunford — Pettis operator      306 309
Operator, factorization      see "Factorization"
Operator, integral operator      225
Operator, maximal monotone operator      119 132
Operator, monotone operator      119
Operator, norm attaining operator      388 396
Operator, nuclear operator      143 225
Operator, weakly compact      132 258 259 260
Order dentable      423 430
Order, partial order      48 152 174 176 183 192 200 380 403 422
Order, weakly compact order interval      426 see "Dilation" "Edgar" "Separable
Orthogonal      165 440
Partial      see "Order"
Pedual      433
Pedual, unique normed predual      163 164 166
Perfect probability space      301 302
Pettis integrable      299 300 302 308 310 311 347
Pettis integral      298 299 301
Pettis Integral Property (PIP)      300 362
Pettis norm      299
Pettis, $\mu$ -Pettis Integral Property ( $\mu$ -PIP)      300 362
Pettis, indefinite Pettis integral      300
Pointed slice      61 62
polar      140
Positive charge      61
Pre compact      see "Weakly"
Probability space      1
Projection (of norm one)      164 166
Property (**)      112 114
Pure, $\varepsilon$ -pure      21
Pure, (x, $\varepsilon$ ) pure      21
Quasi interior point      423
Quasi-martingale      see "Martingale" "Decomposition"
Quasicomplete (locally convex space of type (BM))      419
Radon space      301
Radon — Nikodym Property (RNP)      15 21 30 31 33 49 50 55 57 58 60 67 73 74 75 76 77 91 95 96 93 102 111 114 131 132 137 149 160 161 164 169 172 132 193 225 238 239 240 248 259 267 293 304 313 314 323 332 347 369 371 376 334 396 414 423 425
Radon — Nikodym Property (RNP) for ( $\Omega$ ,F,P)      15 19 31
Radon — Nikodym Property (RNP), super Radon — Nikodym      34 35
Radon — Nikodym Property (RNP), weak Radon — Nikodym Property (WRNP)      298 303 304 305 306 308 309 310 313 314 401
Radon — Nikodym theorem, weak* version      366
Reflexive      74 132
Reflexive, super-reflexive      34 35 36
Representable      see "Finitely"
Residual      117
Riesz Decomposition Lemma 6.4.3      205 211 212 428 437
Ryll — Nardzewski Fixed Point Theorem      50
Schur property      241 250 259 262 290
Schur Property, strong Schur Property      267 290
Semi-embedding      77
Semi-embedding, semi-embeds      77 79 257
Separable extremal      see "Measure"
Separable extremal, ordering      171 181
Separably determined property 31 (Theorem 2.3.6 parts 2 and 3)      60 298
Separation constant      402
Series, transfinite      348
Simple function      3
simplex      204 205 207 239 420
Slice      23
Slice of arbitrarily small diameter      23 31 50
Slice, weak* slice      52
Slice, weak* slice of arbitrarily small diameter      54
Slice, weak* slice of arbitrarily small p -diameter      122 131
Slicing point      61 62 64 65

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