Lukes J., Maly J., Zajicek L. — Fine Topology Methods in Real Analysis and Potential Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Lukes J., Maly J., Zajicek L. — Fine Topology Methods in Real Analysis and Potential Theory

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Название: Fine Topology Methods in Real Analysis and Potential Theory

Авторы: Lukes J., Maly J., Zajicek L.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 472

Добавлена в каталог: 18.08.2008

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Предметный указатель

-extension theorem      112 263 266 311
$B_1-B_{12}$ differentiation bases      163—167
$G_{\delta}$ -insertion property      22 57 58 62 64 66 117 135 143 145 157 179 190 237 249 253
$G_{\delta}$ -measurable function      55
$\mathcal{P}'$ -space      424 430—433
$\mathcal{P}^c$ -bounded      348
$\mathfrak{P}$ -harmonic space      328 330 331 346 347 360—364 383 396 412
$\nu(U)$ -topology      380 382 383 412 424 428 429
$\sigma$ -approximately continuous function      270 271 283 285 286
$\sigma$ -derivative      283
$\sigma$ -lower Lebesgue bounded function      284
$\sigma$ -regular sequence of intervals      283
$\sigma$ -superdensity topology      192 193 197 270
$\sigma$ -topological space      91 94 119 120 247
$\sigma$ -topology      90 94 119 120 247 342 411
(Ba l)-condition      119 180 183 184 293
(bFL)-condition      42
(tFL)-condition      47
a-modification      231—239 270
a-topology      231—239 270
a.e.-modification      230—239 249
a.e.-topology      230—239 249
Absorbent set      359
Abstract category density topology      213 218 221 253
Abstract density topology      212 213—222 224—226 250—254
Abstract in-between theorem      71—75 77—81 95 116 128 280
Ambivalent function      65
Ambivalent set      65 240
Angle differentiation basis      166 179 180 293
Approximate continuity      1 45 63 75 122 149 150 152 157 200 237 260—276 285 320
Averaging principle      318
Axiom of $\tau$ -lower semicontinuous regularization      329 408 429
Axiom of broken ellipticity      363
Axiom of upper directed sets      329 408 429
Axiom, domination = D      360 362 381 421
b-closed set      5
b-topology      5
Baire one function      54—69 73—78
Baire property      171
Baire space      86 222 136—140 192 236
Balayage      222 253
Balayaged measure      351 352
Band      361
Base of a set      333 352
Base operator      5 333
Base operator, compatible with measure      196 204 208 253 277
Base operator, essential      21
Base operator, fine      28
Base operator, ideal      22
Base operator, idempotent      8
Base operator, strong      8
Base operator, z-admissible      22
Base operator, z-ideal      22
Bauer’s minimum principle      355 387 417
Berg’s theorem      344 345
Binormality      85 25
Bitopological boundary      389
Bitopological space      85 92 93
Bliedtner — Hansen lemma (=Prop. 11.7)      352 354 426
Blumberg space      240 141 142 151 236 237 246 364
Boundary bitopological      389
Boundary function      255 287 288 291 292 301 309 310 313
Boundary topology      255 257 301 307 311 313 317
Bounded lower $\mathcal{P}^c$       348
Brelot property      362
Capacity      408 415 421
Categorial lifting      226 228
Choquet boundary      387
Choquet’s lemma      338
Closure operation      7
Cometrizable topology      133 135 188 247 343
Complete Lusin — Menchoff property of base      103 104 105 108 196—199 201 202 233 275
Complete Lusin — Menchoff property of topology      86 88 90 93 98 109 113 114 118 129 151 192 196—199 201 202 233 237 252 255 25B 267 311 343 363
Condition, (*)      22
Condition, (Ba 1)      179 180 183 184 293
Condition, (bFL)      49—54
Condition, (tFL)      47 49—54
Condition, (W)      289 291 293 294 295 298 306 310
Condition, countable chain = (CCC)      19 182
Condition, essential radius      66 67 183 294
Condition, r-basis (B)      241 244 275
Condition, strong essential radius      67 293
Condition, Tietze’s      92 95
Condition, Urysohn’s      91 101
Cone, standard H-=      329 330 332 344 353 354 360 377
Contingent topology      98 258 259 311 312
Convergence theorem      336
Countable chain condition (CCC)      19 182
Crosswise topology      7 40 45 67 68 137 138
Cube differentiation basis      165 179 180 186 198
de Possel differentiation basis      206 214
Denjoy — Stepanoff theorem      171 172 218
Density point      148 152 164 208
Density theorem      148 164 168 172 173 208
Density topology      1 88 92 93 146 148 151 156 158 160 161 237 261 273
Density topology, determined by a differentiation basis $\mathcal{L}$       163—189 198 205 228 244 273 275 276
Density topology, determined by a filter differentiation basis $\mathcal{F}$       204 205 208 210 215
Density topology, determined by a lower density      208 209
Derivative, approximate      272 297 299
Derivative, preponderant      297 298
Derivative, qualitative      300
Differentiation basis      162 179 180 198 205 244
Differentiation basis, angle      166 179 180 293
Differentiation basis, cube      162 179 180 186 198
Differentiation basis, de Possel      206 214
Differentiation basis, filter      201 215 216 226
Differentiation basis, ideal      166 179 180
Differentiation basis, incomplete symmetric      167 179 180 185 187 198
Differentiation basis, interval      165 179 180 198 201 275
Differentiation basis, Morse      207 213 247
Differentiation basis, net      167 179 180 206
Differentiation basis, of Morse type      165 179 180 198
Differentiation basis, rectangle      165 179 180 201
Differentiation basis, right density      166 179 180 184
Differentiation basis, superdensity      166 179 180 192
Differentiation basis, symmetric      164 179 180 186 193 198 201 276
Dirichlet problem      2 327 355 356 430
Dirichlet problem, fine      402
Dirichlet problem, incomplete fine      400
Dispersion point      152 170 181
Domination axiom D      360 362 381 421
Eilenberg — Saks theorem      267 269
Elliptic space      359 360
Essential base operator      31
Essential radius condition      66 67 183 294
Evanescent family      408 409 415 420 422
Evans function      348 349
E’(U) - bounded function      431 432
Filter differentiation basis      203 215 216 226
Fine base operator      38
Fine boundary topology      255 257 301 307 311 313
Fine Dirichlet problem      402
Fine exhaustion      404
Fine sheaf property      381
Fine superfunction      390 391 394
Fine topology      38 43
Fine topology in potential theory      3 318 321 325 332 341 343 345 358 360—364 382
Finely classical solution      394
Finely harmonic function      367 379 398
Finely hyperharmonic function      367 368 370—375 379 380 383 385 389 396 411 413 414 416 420 421
Finely Keldych set      405 406
Finely regular set      336 337 400 404 406 426
Finely resolutive function      390 391 393 422
Finely superharmonic function      367
Function, $G_{\delta}$ -measurable      55
Function, $\mathcal{M}$ -measurable      57
Function, $\sigma$ -approximately continuous      270 271 283 285 286
Function, $\sigma$ -lower Lebesgue bounded      284
Function, $\tau$ -Lipschitzian at x      242
Function, ambivalent      65

Function, approximately continuous      1 45 63 75 122 149 150 152 157 200 237 260—276 285 320
Function, approximately differentiable      245
Function, B-finely harmonic      424 426 427 431
Function, B-finely hyperharmonic      424 426 427 428 430 431
Function, Baire one      54—69 73—78
Function, boundary      255 287 288 291 292 301 309 310 313
Function, E(U)-lower bounded      422 416
Function, Evans      348 349
Function, E’(U)-bounded      431 432
Function, finely harmonic      367 379 398
Function, finely hyperharmonic      367 368 370—375 379 380 383 385 389 396 411 413 414 416 420 421
Function, finely hyperharmonic in Fuglede s sense      367
Function, finely resolutive      390 391 393 422
Function, finely superharmonic      367
Function, fundamental caloric      322
Function, fundamental harmonic      317
Function, harmonic      318 327 348 350 351
Function, honorary Baire two      58 59 68 310 312
Function, hyperharmonic      324 328 348 349 355 368 370
Function, Kopcke      260—262
Function, lower $\mathcal{P}'$ -bounded      424 430
Function, lower $\mathcal{P}^c$ -bounded      348
Function, lower Lebesgue bounded      263 264 274
Function, pointwise finely hyperharmonic      367 369 373 374 386 413 414
Function, Pompeiu      2 260
Function, quasi-continuous      408 412
Function, quasi-l.s.c.      408—416
Function, separately continuous      58 138 306 311
Function, strongly approximately continuous      165 200 271 276 307 308
Function, super-mean-valued      319
Function, superharmonic      3 324 325 328 350
Function, u-continuous      329
Function, U-quasi-t-continuous      431
Function, universally continuous      329 350
Function, upper Lebesgue bounded      263
Function, weakly $\sigma$ -approximately continuous      2§2 284 286
Fundamental caloric function      322
Fundamental harmonic function      317
Generator      334 339 351
H-cone, standard =      329 330 332 344 353 354 360 377 424 428
Harmonic function      318 327 348 350 351
Harmonic measure      355
Harmonic space      328 330 331 347 412
Hausdorff — Kempisty method      115 127 132
Honorary Baire two function      58 59 68 310 312
Hyperharmonic function      324 328 348 349 355 368 370
Ideal base operator      72
Ideal differentiation basis      166 179 180
Ideal topology      22 50 138 141 218 251 253
Idempotent base operator      8
Incomplete fine Dirichlet problem      400
Incomplete symmetric differentiation basis      167 179 180 185 187 198
Increasing family      329
Increasingly dense set      330
Insertion property      57 140
Interval differentiation basis      165 179 180 198 201 275
Irregular point      397 398 406
Jarnik — Blumberg method      287 296 300
Keldych operator      405 406
Keldych set      403
Keldych theorem      406
Key lemma      334 340
Kopcke function      260—262
Kuratowski closure operator      8
L-cone      70—72 119
Lebesgue point      263
Lebesgue spine      323
Lifting      223—229 254
Lifting topology      223 224—228 251 253
Lifting, categorial      226 228
Lifting, on $(X, \Sigma, \mathcal{N})$       226—229
Lifting, strong      254
Lower $\mathcal{P}'$ -bounded      424 430
Lower $\mathcal{P}^c$ -bounded      348
Lower density      207 217 220 223 226 251
Lower Lebesgue bounded function      263 264 274
Lower semicontinuous regularization      408 332 376
Lusin — Menchoff property of $\sigma$ -topology      100 247 342
Lusin — Menchoff property of base      103_—106 196—199 201 233 240
Lusin — Menchoff property of topology      85 89 90 98 99 101 116 117 120 121 125 126 133 134 196—199 201 233 245 247 248 257 271 343
M-modification      107 110 113 268
M-property      137 138
Measurable cover      163
Measurable kernel      162
Measure sweeping property      353 429
Measure, balayaged      351 352
Measure, harmonic      355
Minimum principle      430
Minimum principle, Bauer’s      355 387
Minimum principle, quasi      421
Modification, $\beta$ -=      31
Modification, a-=      231—239 270
Modification, a.e.-=      230—239 249
Modification, M-=      107 LL0 113 268
Modification, principal =      427
Modification, r-=      240—249
natural order      329 377
Natural topology      380 424
Net differentiation basis      167 179 180 206
Newtonian potential      311 320 322 325 350
Ordinary density topology      51 167 181 188 189 237 239 245—247
Perfect Lusin — Menchoff property      96 97 117
Perfectly binormal space      95 96 119
Perron method      355
Perron solution      3 356 396 401 430
Perron upper solution      388
Point, dispersion      152 170 181
Point, irregular      397 398 406
Point, Lebesgue      263
Point, of density      148 152 164 208
Point, regular      3 393 397 399
Point, semiregular      397 398
Pointwise finely hyperharmonic function      367 369 373 374 386 413 414
Polar set      339 340 361 431
Potential      328 348 349 350 393
Potential, heat      222
Potential, logarithmic      323 325
Potential, Newtonian      317 320 322 325 350
Potential, strict      250 393
Preponderant derivative      297 298
Principal modification      427
Principal operator      427
Principal solution      405
Property, $G_{\delta}$ insertion      22 57 58 62 64 66 117 135 143 145 157 179 190 237 249 253 343
Property, (K)      20
Property, Baire      171
Property, complete Lusin — Menchoff of base      103 104 105 108 196—199 201 202 233 275
Property, complete Lusin — Menchoff of topology      86 88 90 93 98 109 113 114 118 129 151 192 196 197—199 201 202 233 237 252 255 258 267 311 343 363
Property, fine sheaf      381
Property, insertion      57 140
Property, Lusin — Menchoff of $\sigma$ -topology      100 247 342
Property, Lusin — Menchoff of base      103—106 196—199 201 233 240
Property, Lusin — Menchoff of topology      85 89 90 98 99 101 116 117 120 121 125 126 133 134 196—199 201 233 245 247 248 257 271
Property, M      137 138
Property, measure sweeping      353 429
Property, perfect Lusin-Menchoff      96 97 117
Property, quasi-Lindelof      17 18 148 182 218 248 344 361
Property, Riesz decomposition      329 377 429
Property, Slobodnik      136 137 138
Property, Zahorski      86 90 92 101 126 260 272
Qualitative derivative      300
Quasi-continuous function      408 412
Quasi-Lindelof property      17 18 148 182 218 248 344 361
Quasi-minimum principle      421
Quasi-open set      411
Quasi-solution      418 419
Quasi-superfunction      419 420 422
r- $\sigma$ -topology      247 248 274 275
r-basis set      240
r-modification      240—249 275

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