Hewitt E., Stromberg K. — Real and abstract analysis: a modern treatment of the theory of functions of a real variable :: Электронная библиотека попечительского совета мехмата МГУ

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Hewitt E., Stromberg K. — Real and abstract analysis: a modern treatment of the theory of functions of a real variable

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Название: Real and abstract analysis: a modern treatment of the theory of functions of a real variable

Авторы: Hewitt E., Stromberg K.

Аннотация:

Hewitt E., Stromberg K. Real and abstract analysis (Springer, 1965, 1975 printing)(ISBN 0387901388)

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1975

Количество страниц: 486

Добавлена в каталог: 07.02.2014

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Предметный указатель

Invariant mean on $\mathfrak{B}^{r}(R)$       359
Inverse of a relation      7
Inversion of Fourier transforms      409
Irregular measure      185
Isolated point      70
Isometry      77
Isomorphic rings      33
Isomorphism      33
Isomorphism, order      27
Iterated integral      385
Iterated integrals on infinite product spaces      439
Jensen’s inequalities      202
Jessen, B.      373 375 439 441 443
Jewett, R. I.      101
Jordan content      121
Jordan decomposition of a complex measure      309
Jordan decomposition of a finitely additive signed measure      338
Jordan decomposition of a signed measure      307
Jordan decomposition theorem      266
Jordan, C.      121
K $\ddot{o}$ nig’s theorem      27
Kakutani, S.      137 453
Kernel, Abel’s      407
Kernel, Dirichlet’s      292
Kernel, Fej $\acute{e}$ r’s      292 408
Kernel, Gauss’s      408
Kernel, Poisson’s      301
Kernel, positive      400
Kre $\breve{\imath}$ n’s extension theorem      220
Kronecker’s delta      11
Lattice of functions      82
Lattice of sets      148
Law of Large Numbers, strong      447 449
Law of large numbers, weak      452
Law, zero-one      443
Leach, E. B.      232
Least upper bound in an ordered field      44
Lebesgue decomposition for decomposable measures      341
Lebesgue decomposition theorem      326
Lebesgue definition of measure      121
Lebesgue Differentiation Theorem      264
Lebesgue dominated convergence theorem      172 174 185
Lebesgue integral      164
Lebesgue integral as an extension of the Riemann integral      184
Lebesgue integral sets      128
Lebesgue integral, fundamental theorem of the integral calculus for      285
Lebesgue integral, linearity of the      169
Lebesgue measurable function      149
Lebesgue measure, extensions of      137
Lebesgue measure, invariant extension of      359
Lebesgue measure, uniqueness of      185
Lebesgue outer measure      120
Lebesgue points for a function      278
Lebesgue set for a function      278
Lebesgue singular function      113
Lebesgue sums      183
Lebesgue — Radon — Nikod $\acute{y}$ m derivative      328
Lebesgue — Radon — Nikod $\acute{y}$ m theorem      315
Lebesgue — Radon — Nikod $\acute{y}$ m theorem for complex measures      323
Lebesgue — Radon — Nikod $\acute{y}$ m theorem for decomposable measures      318
Lebesgue — Radon — Nikod $\acute{y}$ m theorem for regular measures      323
Lebesgue — Radon — Nikod $\acute{y}$ m theorem, examples concerning      340
Lebesgue — Stieltjes integrals, integration by parts for      419
Lebesgue — Stieltjes measures      330
Lebesgue — Stieltjes outer measures      120
Lebesgue, Henri      113 121 158 171 264 267 276 277 294
Left continuous      111
Left derivative      257
Left hand limit      111
Levi theorem, generalized      118
Levi, B.      172
Levi’s theorem      172
Limit inferior      76
Limit of a sequence      62
Limit point      56
Limit, left hand      111
Limit, right hand      111
Limits of continuous functions, pointwise      79
Limits of measures, setwise      339
Linear algebra      82
Linear basis      18
Linear dimension of a vector space      31
Linear functional      211
Linear functional, multiplicative      114 365
Linear functional, nonnegative      114 220
Linear functional, outer measure induced by a nonnegative      120
Linear functionals on $\mathfrak{L}_{1}(R)$ , multiplicative      417
Linear functionals on Hilbert spaces, bounded      248 255
Linear independence      17
Linear operator      210
Linear operator, adjoint of a      221
Linear ordering      8
Linear space      17
Linear space, completion of a normed      221
Linear space, normed      83
Linear span      19
Linear transformation      210
Linear transformation, bounded      210
Linearity of the integral      169 171 174
Linearly ordered set      8
Lipschitz condition of order a      270
Littlewood, J. E.      422
Locally almost everywhere      122
Locally compact space      74
Locally integrable function      186
Locally null function      123
Locally null set      122 346
Locally uniformly convex Banach spaces      233
Lower bound      13
Lower semicontinuous function      88
Luzin, N. N.      159 288
Luzin’s theorem      159
Mapping      9
Mapping, contraction      78
Mappings of measurable sets      150 269 288 297
Martingale in the wide sense      253
Martingale theorems      369 371 375
Maximal element      13
Maximal theorem, Hardy — Littlewood      424 425 426
Maximality principle, Hausdorff      14
Mayrhofer, K.      121
McShane, E. J.      229
Mean Value Theorem for integrals, first      420
Mean Value Theorem for integrals, second      420
Measurable dissection      164
Measurable function      149 154
Measurable function, Borel      149 187
Measurable function, Lebesgue      149
Measurable rectangle      379
Measurable sections, nonmeasurable sets with      393
Measurable set      127
Measurable sets      138
Measurable sets, Lebesgue      128
Measurable sets, mappings of      150 269 288 297
Measurable space      149
Measurable subsets, measures on      161
Measure      126
Measure space      126
Measure space, $\sigma$ -finite      127
Measure space, complete      155
Measure space, completion of a      155
Measure space, decomposable      317
Measure space, decomposition of a      317
Measure space, finite      127
Measure space, integrals on the completion of a      186
Measure space, nondecomposable      349
Measure spaces, infinite products of      429
Measure, $\sigma$ -finite      127
Measure, Borel      329
Measure, complete      155

Measure, complex      304
Measure, complex regular Borel      360
Measure, convergence in      156
Measure, countably additive      126
Measure, counting      127
Measure, decomposable      317
Measure, degenerate      127 186
Measure, derivative of a signed      366
Measure, derivative of an absolutely continuous      328
Measure, Dirac      120
Measure, extending a      162
Measure, extensions of Lebesgue      137
Measure, finite      127
Measure, finitely additive      126
Measure, Hausdorff      145
Measure, integral relative to a complex      312
Measure, invariant extension of Lebesgue      359
Measure, irregular      185
Measure, Jordan decomposition of a complex      309
Measure, Jordan decomposition of a finitely additive signed      338
Measure, Jordan decomposition of a signed      307
Measure, Lebesgue’s definition of      121
Measure, metric of convergence in      182
Measure, negative variation of a signed      307
Measure, nonnegative set for a signed      305
Measure, nonpositive set for a signed      305
Measure, outer      126
Measure, positive variation of a signed      307
Measure, Radon      114
Measure, regular      177 185
Measure, regular finitely additive      364
Measure, Regular outer      143
Measure, signed      304
Measure, support of a      122
Measure, total variation of a complex      308
Measure, total variation of a signed      307
Measure, uniqueness of Lebesgue      185
Measures on image sets      161
Measures on measurable subsets      161
Measures on nonmeasurable subsets      161
Measures on R, regular Borel      329
Measures, absolutely continuous      312
Measures, continuous      334
Measures, continuous images of      180
Measures, extensions of      141 148
Measures, finitely additive      354
Measures, infinite product      432
Measures, integrals for finitely additive      355
Measures, Lebesgue decomposition for decomposable      341
Measures, Lebesgue — Stieltjes      330
Measures, metric outer      144
Measures, product of two      384
Measures, purely discontinuous      334
Measures, regularity of product      389
Measures, setwise limits of      339
Measures, singular      326
Measures, zero-one      358
Metric      59
Metric of convergence in measure      182
Metric outer measures      144
Metric space      59
Metric space, bounded set in a      66
Metric space, complete      67
Metric space, completion of a      77
Metric topology      60
Metric, discrete      59
Metric, Euclidean      59
Minimal element      13
Minkowski’s inequality      191
Monotone Convergence Theorem      172
Monotone convergence theorem, generalization of      118
Monotone family      380
Monotone function      105
Monotone function, differentiability of      264
Monotone sequence in       76
Multiplication, scalar      17
Multiplicative linear functionals      114 365
Multiplicative linear functionals on $\mathfrak{L}_{1}(R)$       417
Negative variation of a signed measure      307
Neighborhood      56 60
Net, differentiation on a      373
Non — Archimedean ordered field      46
Nondecomposable measure space      349
Nondecreasing function      105
Nondecreasing function, normalized      112 330
Nonincreasing function      105
Nonmeasurable sets      135 146
Nonmeasurable sets with measurable sections      393
Nonmeasurable sets, measures on      161
Nonnegative linear functional      114 220
Nonnegative linear functional, outer measure induced by a      120
Nonnegative set for a signed measure      305
Nonpositive set for a signed measure      305
Norm      83
Norm $\mathfrak{L}_{\infty}$       346
Norm, $\mathfrak{L}_{p}$       188
Norm, operator      210
Norm, total variation      271
Norm, uniform      83
Normal numbers      452
Normalized Hermite functions      245
Normalized nondecreasing function      112 330
Normed algebra      83
Normed linear space      83
Normed linear space, completion of a      221
Nowhere dense set      68
Nowhere differentiable functions, continuous      258
Null function      123
Null function, locally      123
Null sequence      38
Null set      122
Null set, locally      122 346
Number, cardinal      19
Number, ordinal      28
Numbers, complex      2
Numbers, expansion of real      46 47
Numbers, extended real      54
Numbers, field of complex      48
Numbers, normal      452
Numbers, order relation for cardinal      20
Numbers, rational      2
Numbers, real      2
Numbers, strong law of large      447 449
Numbers, weak law of large      452
One-to-one relation      9
Onto function      10
Open ball      60
Open cover      62
Open interval      54
Open mapping theorem      215
Open set      55
Open set in       55 69
Open, relatively      61
Operator norm      210
Operator, adjoint of an      221 251
Operator, linear      210
Operators, algebra of      251
Order isomorphism      27
Order relation for cardinal numbers      20
Order topology      79
Order type      27
Ordered field      35
Ordered field, Archimedean      37
Ordered field, complete Archimedean      44
Ordered field, completion of an      38
Ordered field, Dedekind cut in an      46
Ordered field, greatest lower bound in an      44
Ordered field, infimum in an      44
Ordered field, least upper bound in an      44
Ordered field, non — Archimedean      46

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