Fuchssteiner B., Lusky W. — Convex Cones (North-Holland Mathematics Studies) :: Электронная библиотека попечительского совета мехмата МГУ

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Fuchssteiner B., Lusky W. — Convex Cones (North-Holland Mathematics Studies)

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Название: Convex Cones (North-Holland Mathematics Studies)

Авторы: Fuchssteiner B., Lusky W.

Аннотация:

The aim of this book is to outline an elementary theory of linear functional on convex cones, but convex cones are here taken in a slightly more general way than usual, they need not be imbedded in a vector space. In consequence, we do not have a general cancellation law for the addition. Typical examples for the cones we have in mind are R = R и {- } or the upper semicontinuous R- valued functions on some topological space. Accordingly, linear functionals on such cones are allowed to attain values in R instead of R . This generality has advantages with respect to extensions of linear functionals.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1981

Количество страниц: 438

Добавлена в каталог: 16.08.2015

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Предметный указатель

$Cone(\mu)$       221
$Conv_{B}(X)$       297
$Conv_{C}(X)$       300
$Face(\mu)$       221
$F^{*}_{+}$       117
$F^{*}_{n}$       113
$f_{-}$       107 179
$L^{p}(M)$       393
$Maxa_{\alpha, \beta}(K)$       259
$M_{x}$       262
$Prob(\Omega)$       274
$P_{\lambda}$ -space      74
$UC^{+}_{\inf}(X)$       192 212 235
$USC(\Omega)$       38 227
$\bar{R}$ -valued representing measure      308
$\Gamma$ - invariant      252
$\sigma-$ completion      233 382
$\tilde{Ch}$ (K)      259
$\tilde{Max}(K)$       259
(F, $\prec$ )*, $(F, \prec)^{#}$ , $(F, \prec)_{#}$ ,      102
A(K)      267
Absorbing functional      149
Abstract integral      386
Adapted cone      237
Additive      3
Affine      35 90 267 283
Affine interposition      34
AL-cone      154
Alexandrov      248
Alexandrov compactification      338 341
Alexandrov — Glicksberg theorem      313 330
Algorithm      80 82
AM- cone      154
AM- space      89 157 162
Andenaes      80
Ando      111
Anger      78
Archimedean      170
Arithmetic mean      24
Ascoli's theorem      342
Asimov      111
Aumann      75
B(X), $B_{0}(X)$       381
Baire (X)      382
Baire measure      228 239 282 296
Baire space      171 335
Baire's category theorem      100 171 310
Baire-measurable      99 301 392
Baker      173
Banach      72 73 248
Banach lattice      150
Banach Steinhaus theorem      72
Bauer      76 258 286 303 304
Bauer-simplex      286 378
Bd $\sum(X)$       382
Bd $\sum_{+}(X)$       399
Bernau      173
Bernstein      343
Bimeasure      49
Binary intersection property      72 77
Birkhoff — Ulam theorem      171
Bishop      21 269 303 304
Blackwell      173
Bleier      173
Boboc      304
Bochner      368
Bochner — Weil theorem      363 378
Bochner's theorem      375
Bonsai      1 303
Bor(X)      382
Bou      74 78
Boundary      40 252 255 288
Bourgin      250
Buck      248
C*- algebra      170 358
Cancellation law      8 107
Cartier      172
Cartier — Fell — Meyer Theorem      88 121
Central limit theorem      371
CHARACTER      88 139 158 270 276 285 315 350 363
Chatterji      199 249
Choquet      76 173 249 269 303 304 335
Choquet boundary (Ch(K))      259 287 298 300
Choquet — Meyer Theorem      281
Choquet's theorem      268 312
Choquet-order      275
Choquet-simplex      88 173 286
Cignoli      82
co(X)      256
Commodity set      58 60
Common sense      65
Compatible      62 66
Complementary set      318
Completely monotonic function      341
Complex linear      34 355
Concave      35
Cone      6
Conrad      173
Consumer set      56
consumption      54 57 60
Consumption measure      56
Continuous order relation      243
Conv(K)      253 267
Convex combination      256
Convex cone      6
Convex function      34 253
Convex hull      125 257 297
Convex set      8 33 90 102 125 253 311 335
Convolution      364
Cornea      304
Cotlar      75
Countable covering      202 224
Countable decomposition      177
Countable intersection property      230
Daniel      1 246
Daniell — Stone theorem      203 209 220 246 400
Davies      304
de Leeuw      269 304
Decomposable      179
Decomposition property      203
Decomposition theorem      184
Demand measure      61 66
Dies tel      249
Dinges      75
Dini boundary      287 291
Dini character      315
Dini cone      189 203 210 268 287 291 308 328
Dini continuous      210 232 314
Dini lattice      198
Dini's lemma      164 189 240
Dini-condition      189 268
Dirichlet state      220
Disintegration Theorem      42 44 83
Distribution plan      62 66
Distributive law      101
Dominating Extension Theorem      11
Donner      78
Downwards directed      186
Edgar      250
Edward's separation theorem      171
Edwards      111 171 304 335
Ellis      111
Envelope      103 277
ex(K)      256 267
Exposed element      80
Exposed selfmap      252
Extension theorem      12
Extremally disconnected      75 97 157
Extreme point      80 142 170 256 267 340 378
Extreme ray      142

F(X)- exposed      253
F- compact, F- compactification      315
F- Hewitt — Nachbin-space      315
F- pseudocompact      315
F- real compact, F- realcompactification      315
Face      220 226
Farkas' Lemma      29
Fell      172
Finite covering      27
Finite Decomposition Theorem      17
Finite Sum Property (FSP)      88 107 222
First countable      302
Fischer      72
fixpoint      254
Fixpoint boundary      343
Flow Theorem      49 51
Ford — Fulkerson Theorem      54 84
Fourier-cotransform      365
Fourier-transform      365
Free abelian semigroup      25
Free lattice cone      88 122 125 285
Frolik      338
Functional      9
G- anti tone      106
G- montone      106 179
G- order      106 179
G- space      174
Gale      54 84
Gale — Ryser Theorem      54
Gelfand representation      360 378
Gelfand — Naimark theorem      359 378
Gelfandtransform      90 274 351
General character      139
Generalized Hewitt-Nachbin space      313
GENERATED      107 182
Geometric situation      253 267
Glicksberg      248 313
Goodner      73
Goullet de Rugy      198
Greatest lower bound      17
Haar measure      363
Hahn      73
Hahn — Banach property      74
Hahn — Banach separation theorem      33
Hahn — Banach theorem      2 34 72
Hal peri n      75
Hardy      173
Hasumi      75
Helley      72
Herglotz      368
Herve      303
Hewitt      239 248 337 338 339
Hewitt — Nachbin space      313 337
Hewitt's Theorem      201
hilbert      72
Hilfsfunktional      307
Homogeneous      9
Hopf — Kolmogorov Extension Theorem      400
Hustad      75
Hypolinear      78
Import capacity      56
Improved Representation Theorem      292
Infinitely divisible      345 371
Injective element      74
Integer-valued flow      85
Interposition Theorem      111
Inverse preorder      102
Invertible      89
Involution      355 364
James' theorem      287
Jensen measure      22 23 303
Jordan decomposition      28 215
Kadi son      170
Kadison — Kakutani — Stone Theorem      170
Kakutani      89 157 162 174 248
Kakutani — Krein — Stone — Yosida Theorem      87 95 157 164 170
Kantorovitch      73
Katetov      338
Katetov — Nachbin Theorem      244
Kaufmann      75
Kelley      75
Kendall      345
Klee      172
Koenig      28 29 37 44 75 76 79 84
Kolmogoroff      379
Korovkin      167
Korovkin family      167 176
Korovkin's Theorem      89 167 175
Kranz      75
Krein — Milman Property      199
Krein — Milman theorem      80 257 267
Laplace equation      40
Lattice cone      93 101
Lattice cone homomorphism, isomorphism      120
Lattice cone subhomomorphism      123
Lattice homomorphism      74 94 120 196
Lattice state      87
Lattice-generated cone      136 145
Lebesgue decomposition theorem      395
Lebesgue dominated convergence theorem      385
Lembcke      78
Levy — Khintchine formula      345 376
Lindeloef space      230 298 334 339
Lindenstrauss      77
Linear      9 43 241
Littlewood      173
Localized order structure      43 51
Locally compact Abelian group      363
Loomis      88 100
Loomis — Sikorski theorem      100 400
Mankiewicz      250
Marginal measures      83
Markov      248
Marriage theorem      84
Martingale convergence property      199 249
Mass zero      242
Matthes      400
Max flow - min cut theorem      54 84
max(K)      255 258
Max-boundary      40
Max-stable      189 191 274 291
Maximal F(X)- exposed family      254
Maximal linear functional      140 211 225 281
Maximal measure      275
Maximum point      259
Maximum principle      20 40 256 267
Mazur — Orlicz theorem      34
Meagre      99 307
Measure      383
Meyer      172 304
Minimal fixpoint boundary      81 254
Minimal total demand      64 66
Mokobozki      237 239 304
Monotone convergence property      385
Monotone,      3 43 349 357
Mrowka      338 339
Multiplicative      22 350 355
Multiplicative cone      349
Nachbin      73 74 244 249 337
Nachbin family      247
Natural preorder      106 155
Negative cone      107
Negatively generated      107 151
networks      49 54 82
Neumann      44 247 287
Neutral element      2 8 22
Norm Theorem      13
Normed linear functional      213 242
Order bounded      2 96
Order complete      2 96 305 396

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