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Kechris A.S., Louveau A. — Descriptive Set Theory and the Structure of Sets of Uniqueness
Kechris A.S., Louveau A. — Descriptive Set Theory and the Structure of Sets of Uniqueness



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Название: Descriptive Set Theory and the Structure of Sets of Uniqueness

Авторы: Kechris A.S., Louveau A.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 387

Добавлена в каталог: 17.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$H^{(n)}$-set      81
$M^p$-set      227
$M^p_0$-set      268
$M_0$-set      118
$M_1$set      211
$U^{'}$-set      182
$U^{'}_0$-set      271
$U^{'}_1$-set      211
$U_0$-rank      281
$U_0$-set      118
$U_0$-thin set      238
$U_1$-set      211
$\epsilon$-almost period      186
$\mathcal{U}$-set      24
$\mathcal{U}_0$-set      76
$\mathscr{M}$-set      24
$\mathscr{M}_0$-set      76
$\sigma$-ideal of closed sets      131
$\sigma$-ideal of sets      131
$\underline{\Delta}^1_1$-Selection Theorem      149
$\underline{\prod}^1_1$-complete set      111
$\underline{\prod}^1_1$-hard set      127
$\underline{\prod}^1_1$-rank      140
Absolute continuity of measures      77
Absolutely convergent Fourier series      33 52
Algebraic integer      84
Almost comeager set of probability measures      297
Almost periodic (a.p.) pseudomeasure      185
Almost periodic at x pseudomeasure      188
Ambiguous class      106 107
Analytic (or $\underline{\sum}^1_1$ or A) set      106
Annihilator      159
B-derivative      197
Baire space      112
Banach Theorems on w*-closure      153 154 156
Banach — Alaoglu theorem      151
Band of measures      310
Barycenter (of a measure)      169 310
Bary’s Theorem on countable unions of closed $\mathcal{U}$-sets      41
Basis of a $\sigma$-ideal      194
Basis Theorem for $U_0$      274
Borel Basis Problem for U      221
Borel co-basis      265
Borel Determinacy Theorem of Martin      120 136
Borel hierarchy      109
Borel set      104
Boundary of a set      223
Boundedness Theorem for $\prod^1_1$-ranks      148
Branch of a tree      112
Calibrated $\sigma$-ideal      207
Cantor (1/3-)set      38
Cantor Uniqueness Theorem      30
Cantor Uniqueness Theorem for countable closed sets      32
Cantor — Bendixson derivative      32
Cantor — Bendixson rank (classical)      201
Cantor — Bendixson rank associated to B      198
Cantor — Lebesgue Lemma      29
Capacity      293 314
Capacity, continuous      293
Carlet — Debs Theorem      44
Category Problem      48
Characterization Problem      48
Choquet Capacitability Theorem      315
Co-basis (Borel)      265
Coanalytic (or $\underline{\prod}^1_1$ or CA) set      106
Comeager (= complement of first category)      294
Completeness method      110
Concatenation of sequences      111
Concentrates (measure on a set)      310
Contiguous intervals of a closed set (= components of its complement)      49
Convex closed envelope      311
Convex cone      284
Convolution of elements of $\ell^1$      52
Convolution of measures      237
Davis’ Theorem      120 136
de la Vallee — Poussin Theorem      41
Debst — Saint Raymond Non-Basis Theorem for U      261
Debst — Saint Raymond Theorem on $\mathcal{U}_0$      289 290
Debst — Saint Raymond Theorem on $\mathcal{U}_0$, alternative proof of      290
Derivative, B-      197
Derivative, Cantor — Bendixson      32
Derivative, Schwarz second      26
Determined game      120
Dichotomy theorem      132
Dirac measure      186
Dirichlet set      338
Dirichlet theorem      338
Dual (class)      105
Empty sequence      111
Envelope, convex closed      311
Envelope, of a class of measures      313
Extension of finite sequences      112
Fejer kernel      238
Finite Borel class      105
Formal product      33
Fourier (— Stieltjes) coefficients of a measure      55
Fourier coefficients of a function      23
Fourier series      23
Fourier series, absolutely convergent      33 52
Function, Riemann      26
Function, smooth at x      31
Function, trapezoidal      57
Function, triangular      57
Game, determined      120
Game, Wadge      119
Goldstme’s Theorem      168
H-set      38
Hausdorff measure      294
Hausdorff metric (on K(E))      117
Hausdorff topology      117
Height of a sequence in a tree      141
Height of a tree      141
Helson constant      246
Helson set      243
Hereditary, class of measures      310
Hereditary, collection of sets      25 131
Herz transform      226
Herz’s Criterion      224
Herz’s Lemma      224
Homogeneous perfect set associated to ($\xi$; $\eta_1$ ... $\eta_k$)      89
Hurewicz Theorem on $K(\mathbb{Q}^{'})$      119
Hurewicz Theorem on $K_{\omega}(E)$      137
Hurewicz Theorem on $\underline{\prod}^1_1$ not $G_{\delta}$ sets      133
Hurewicz-type theorem      133
Ideal of closed sets      131
Ideal of functions in A      174
Ideal of sets      131
Independent set      331
Infimum of measures      317
Initial segment      112
Integer, algebraic      84
Interior problem      47
Interval in $\mathbb{T}$      38
Ivashevt — Musatov Theorem      294
Kaufman’s Theorem on approximating M-sets by $H_{\sigma}$-sets      239
Kaufman’s Theorem on Helson sets of multiplicity      250
Kholshchevnikova’s Theorem      45
Koerner’s Theorem      250
Komlos’ Theorem      325
Kronecker set      333
Kronecker’s theorem      331
Large in $U_0$      322
Length of a sequence      111
Length of a well-founded relation      145
Localization principle for Fourier series      25
Localization principle of Riemann      37
Lusin Separation Theorem      109
Lyons’ Characterization of Rajchman measures      324
M-set      118
Malliavin’s theorem      258
Marcinkiewiczt — Zygmund Theorem      71
Mazur’s theorem      169
Meager (= of the first category)      297
Measure, complex Borel on T      54
Measure, concentrating on a set      310
Measure, positive      56
Menshov’s Theorem      103
Meyer set      328
Milicer — Gruzewska Lemma      77
Minimax lemma      317
Mokobodzki’s theorem      313
Multiplicity set      24
n-translate of a pseudomeasure      185
nbhd ( = open neighborhood)      59
Novikov separation theorem      149
Null set of a measure      267
Order of a subspace      156
Overspill method      149
Parallelepiped in $\mathbb{T}^n$      81
Partial sums of a trigonometric series      21 22
Partition of unity      60
Piatetskit — Shapiro Criterion      82
Piatetskit — Shapiro Decomposition Theorem      213 215
Piatetskit — Shapiro description of U-sets      69 174
Piatetskit — Shapiro rank on $U_1$      211
Piatetskit — Shapiro rank on U      174
Piatetskit — Shapiro Theorem on $H^{(n)}$-sets      82
Piatetskit — Shapiro Theorem that $U_1 \subsetneqq U_0$      258
Pisot number      84
Polish space      104
Privileged Suslin scheme      314
Problem of harmonic synthesis      222
Projective hierarchy      109
Projective set      107
Pseudofunction      54
Pseudomeasure      53
Pseudomeasure satisfying synthesis      302
R-rank      172
Rajchman measure      76
Rajchman multiplication theory      33
Rank      140
Rank, Cantort — Bendixson associated to B      198
Rank, method      110 148
Rank, Piatetskit — Shapiro on $U_1$      211
Rank, Piatetskit — Shapiro on U      174
Rational relative to $2\pi$      39
Reduced nucleus of a trigonometric series      302
Reduction (of a set via a function to another set)      115
Regular matrix      28
Representation theorem for $\underline{\sum}^1_1$ sets      113
Respects inclusion, function      141
Riemann function      26
Riemann localization principle      37
Riemannt — Lebesgue Lemma      30
Riemann’s First Lemma      27
Riemann’s Second Lemma      31
Salemt — Zygmund Theorem      90
Satisfying synthesis, pseudomeasure      302
Schwarz second derivative      26
Schwarz’s lemma      29
Sequentially w*-dense      157
Set "in $M^p_0$"      293
Set of bounded synthesis      348
Set of extended uniqueness      76
Set of interior uniqueness      47
Set of local extended uniqueness      269
Set of local uniqueness      227
Set of multiplicity      24
Set of pure multiplicity      227
Set of pure restricted multiplicity      269
Set of resolution      329
Set of restricted multiplicty      76
Set of synthesis      223
Set of umquness of rank 1      182
Set of uniqueness      24
Set without true pseudomeasure      329
Shrinking method      231
Smooth at x function      31
Solovay Theorem on $[E]_{PS}$      175
Solovay, Kaufman Theorem      123 127
Strategy      120
Strongly calibrated $\sigma$-ideal      238
Strongly convex set of measures      310
Subprobability      309
Summability method      28
Support of a function      62
Support of a measure      67
Support of a pseudomeasure      66
Supported (pseudomeasure by a closed set)      68
Suslin scheme, privileged      314
Suslin’s Theorem      108
Symmetric perfect set of constant ratio of dissection $\xi$      88
Symmetric perfect set with dissection ratios $\xi_1, \xi_2...$      87
Toeplitz conditions      28
Total variation of a measure      54
Trapezoidal function      57
TREE      112
Tree-rank      164
Triangular function      57
Trigonometric polynomial      53
Trigonometric series      21
Trigonometric series, real      21
True $\Gamma$ set      110
U-set      118
U-set of rank 1      182
U-thin set      238
Ultra-thin symmetric sets      103
Uniformly distributed sequence      295
Union Problem      46
Uniqueness set      24
Uniqueness Theorem for Fourier series      54
Universally measurable set      77
Vanishes (a pseudomeasure on an open set)      62
W*-set      295
W-set      322
Wadge game      119
Wadge-type game      135
Weak topology      151
weak*-convergence in PM      68
weak*-sequential closure      153
weak*-topology in general      151
weak*-topology on A      81
weak*-topology on PM      68
Well founded relation      145
Well founded tree      112
Weyl set      322
Weyl’s Criterion for uniform distribution      296
Wiener’s Theorems on A      59
Winning strategy      120
Without true pseudomeasure, set      329
Young's Theorem      45
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