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Авторизация |
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Kechris A.S., Louveau A. — Descriptive Set Theory and the Structure of Sets of Uniqueness |
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Предметный указатель |
-set 81
-set 227
-set 268
-set 118
set 211
-set 182
-set 271
-set 211
-rank 281
-set 118
-thin set 238
-set 211
-almost period 186
-set 24
-set 76
-set 24
-set 76
-ideal of closed sets 131
-ideal of sets 131
-Selection Theorem 149
-complete set 111
-hard set 127
-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 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 -sets 41
Basis of a -ideal 194
Basis Theorem for 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 -ranks 148
Branch of a tree 112
Calibrated -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 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 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 289 290
Debst — Saint Raymond Theorem on , 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 (; ... ) 89
Hurewicz Theorem on 119
Hurewicz Theorem on 137
Hurewicz Theorem on not 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 38
Ivashevt — Musatov Theorem 294
Kaufman’s Theorem on approximating M-sets by -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 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 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 211
Piatetskit — Shapiro rank on U 174
Piatetskit — Shapiro Theorem on -sets 82
Piatetskit — Shapiro Theorem that 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 211
Rank, Piatetskit — Shapiro on U 174
Rational relative to 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 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 " 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 175
Solovay, Kaufman Theorem 123 127
Strategy 120
Strongly calibrated -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 88
Symmetric perfect set with dissection ratios 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 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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