Kuttler K.L. — Modern Analysis :: Электронная библиотека попечительского совета мехмата МГУ

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Kuttler K.L. — Modern Analysis

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Название: Modern Analysis

Автор: Kuttler K.L.

Аннотация:

This book addresses real and abstract analysis, offering a sensible introduction to functional analysis as well as a thorough discussion of measure theory, Lebesgue integration, and related topics. Its topics include basic measure theory in an abstract and concrete form, material on classic linear functional analysis, probability, and basic results used in the theory of partial differential equations. Two different proofs of the central limit theorem are examined as well as a straightforward approach to conditional probability and expectation.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 583

Добавлена в каталог: 08.12.2013

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Предметный указатель

$C^{1}$ functions      68
$F_{\sigma}$ sets      123
$G_{\delta}$       34
$G_{\sigma}$ sets      123
$l^{1}$       140
$L^{1}$ , sequential compactness      244
$L^{p}$ , compactness in      367
$L^{p}(\Omega; X)$       485
$L^{p}_{loc}$       359
$l^{\infty}$       215
$\epsilon$ net      17
$\sigma$ locally finite basis      541
Alexander subbasis theorem      98
Alexandrov’s theorem      520
Algebra of sets      123
Analytic function      546
Apriori estimates      110
Area formula      398
Ascoli — Arzela theorem      23
Axiom of Choice      1—2 169
Axiom of extension      1
axiom of specification      1
Axiom of unions      1
Banach space      205
Banach space, interpolation      469
Banach — Alaoglu theorem      100
Banach — Steinhaus theorem      36
Basic open set      5
Basis      5
Besicovitch covering theorem      263
Bessel potentials      472
Bochner integrable      482
Borel measurable      132 169
Borel measure      154
Borel regular      381
Borel sets      123
Borel — Cantelli lemma      133
Bounded continuous linear functions      35
Brouwer fixed point theorem      557
Calderon — Zygmund decomposition      438
Cantor diagonal process      31
Cantor function      169
Cantor set      169
Caratheodory      149
Caratheodory’s criterion      378
Caratheodory’s procedure      150
Cauchy Schwarz inequality      49
Cauchy sequence      7
Ceasaro mean      61
Central limit theorem      338
Chain rule      64
Change of variables      177 433
Change of variables 1—1 transformation      257
Change of variables general case      259
Characteristic function      135 305
Chi square      348
Clarkson’s inequality      216
Closed graph theorem      39
Closed set      6
Closure of a set      7
Coarea formula      427
Coercive      527
Combinations of measurable functions      130
Compact set      8
Complete measure space      150
Complete metric space      7
Completely separable      7
Completion of a measure space      170
Completion of product measures      196
Conjugate function      509
Continuous function      8
Convergence in measure      133
Convex function      503
Convex functions      214
Convex sets      91
Convolution      212 297
Covariance      305
derivatives      64
Differentiability monotone functions      261
Differential equations      552
Differential equations, global existence      109 121
Differential equations, Peano existence theorem      85
Differential inclusion      528
Dirichlet kernel      47
distribution      355
Distribution function      200 259 436
Divergence theorem      411
Dominated Convergence Theorem      143 487
Dual space      43
Duality maps      47
Eberlein — Smulian theorem      104
Egor off theorem      131
Elementary sets      189
Equality of mixed partial derivatives      70
Equivalence of norms      55
Expected value      304
Fatou’s Lemma      142
Fejer kernal      61
Fisher Neyman criterion      352
Fourier series      46
Fourier transform      295
Fourier transform $L^{1}$       299
Fourier transforms      283
Fubini’s Theorem      176 192 198
Fundamental theorem of calculus, general Radon measures      271
Fundamental theorem of calculus, Lebesgue measure      249
Gamma function      214 376
Gauge function      40
Graves theorem      82
H $\ddot{o}$ lder’s inequality      203
Hahn Banach theorem      41
Hardy Littlewood maximal function      247
Hardy’s inequality      214
Hausdorff and Lebesgue measure      384
Hausdorff dimension      384
Hausdorff maximal principle      40
Hausdorff maximal theorem      529
Hausdorff measures      378
Hausdorff space      6
Heine — Borel theorem      20
Helly’s lemma      56
Helly’s selection theorem      351
Higher order derivatives      68
Hilbert space      49
Hormander condition      440
Implicit function theorem      77
Inner product space      49
Inner regular measure      154
Inverse function theorem      71 84
Isodiametric inequality      371 375
Isometric      494
Iterated integrals      189
James map      44
Jensens inequality      214
Laplace transform      187
Laplace transforms      244
Lebesgue decomposition      241
Lebesgue integral      136 140
Lebesgue measure      171
Lebesgue measure, translation invariance      173
Lebesgue number      251
Lebesgue set      250
Lebesgue Stieltjes measure      168
lim inf      129
lim sup      129
Limit point      6
Lipschitz maps, extension      387

Locally compact      8
Locally convex topological vector space      87
Locally finite      535
Marcinkiewicz interpolation      437
Maximal function measurability      259
Maximal function strong estimates      260
Maximal function, general Radon measures      268
McShane’s lemma      233
Mean      305
Measurable      149
Measurable function      127
Measurable rectangle      189
Measurable representative      490
Measurable sets      126 149
Measure space      126
Metric space      7
Metrizable space      541
Mihlin’s theorem      452
Milman’s theorem      58
Minkowski functional      47 56 92
Minkowski’s inequality      206
Moment generating function      305
Monotone class      124
Monotone Convergence Theorem      136
Morrey’s inequality      361
Multi-index      283
Nagata — Smirnov metrization theorem      544
Nonmeasurable set      169
Normal topological space      6
Nowhere differentiable functions      46
One point compactification      13
Open cover      8
Open mapping theorem      37
Open sets      5
Orthonormal set      60
Outer measure      133 149
Outer regular measure      154
Paracompact space      535
Parallelogram identity      60
Parseval’s Inequality      60
Partial order      40
Partially ordered set      529
Partition of unity      155 539 541
Pettis theorem      478
Plancherel theorem      289
Point of density      259
Pointwise limits of measurable functions      128
polar      509
Polar coordinates      183
Polar decomposition      224
Positive linear functionals      156
Power set      5
Precompact      30
Product measure      191
Product measures and regularity      193
Product rule      361
Product topology      8
Projection in Hilbert space      51
Proper function      503
Pseudomonotone operator      113
Quotient space      469
Rademacher’s Theorem      363
Radon measure      156
Radon Nikodym property      491
Radon Nikodym Theorem, $\sigma$ finite measures      220
Radon Nikodym Theorem, finite measures      219
Random variable, chi square      348
Random vector, characteristic function      305
Random vector, distribution function      304
Random vector, independent      309
Random vector, moment generating function      306
Random vector, normal      335
Random vectors      303
Rao — Blackwell theorem      352
Refinement of a cover      535
Reflexive Banach space      45
Reflexive space, closed subspace of      300
Regular measure      154
Regular topological space      6
Riemann integrable      168
Riemann Stieltjes integral      168
Riesz representation theorem      496
Riesz representation theorem $L^{p}$ , $\sigma$ finite case      230
Riesz representation theorem $L^{p}$ , finite measures      226
Riesz representation theorem $L^{p}$ , non $\sigma$ finite measure space      237
Riesz representation theorem $L^{p}$ , positive linear functionals      156
Riesz representation theorem for $L^{1}$ , finite measures      229
Riesz Representation theorem,       239
Riesz representation theorem, $C_{0}(X)$       240
Riesz representation theorem, Hilbert space      52
Riesz representation theorem, locally compact Hausdorff space      164
Sard’s lemma      256
Schaefer fixed point theorem      121
Schauder fixed point theorem      108
Schroder Bernstein theorem      2
Schwartz class      283
Seminorms      87
Separable space      7
Separation theorem      47
Sequential weak* compactness      103
Shannon sampling theorem      301
Sigma algebra      123
Sigma compact topological space      155
Sigma finite      189
Simple function      135 475
Sobolev Space, embedding theorem      300 368
Sobolev Space, equivalent norms      300
Sobolev Space, extension map      416
Sobolev Space, reflexive space      367
Sobolev Space, trace map      415
Steiner symetrization      373
Stone’s theorem      537
Strict convexity      48
Strongly measurable      475
Subbasis      9
Sufficient statistic      314
Support of a function      154
Surface measure      402
Taylor’s Formula      545
Tempered distributions      293
Tietze extention theorem      31
Topological space      5
Topological vector space dual      89
Total variation      222
Totally bounded set      17
Totally ordered set      529
Triangle inequality      142
Tychonoff fixed point theorem      107
Tychonoff theorem      100
Uniform boundedness theorem      36
Uniform convexity      48 58
Uniformly convex      216
Uniformly integrable      145
Urysohn’s lemma      9
Variational inequality      51
Vector measures      222 490
Vitali convergence theorem      215
Vitali covering theorem      246
Vitali coverings      260
Weak * convergence, Young’s measures      277
Weak convergence      48
Weak derivative      356
Weak topology      98
Weak* measurable      480
Weak* topology      98
Weakly measurable      475
Well-ordered sets      531
Young’s inequality      242

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