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Folland J.B. — Real Analysis: Modern Techniques and Their Applications

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Название: Real Analysis: Modern Techniques and Their Applications

Автор: Folland J.B.

Аннотация:

This book covers the subject matter that is central to mathematical analysis: measure and integration theory, some point set topology, and rudiments of functional analysis. Also, a number of other topics are developed to illustrate the uses of this core material in important areas of mathematics and to introduce readers to more advanced techniques. Some of the material presented has never appeared outside of advanced monographs and research papers, or been readily available in comparative texts. About 460 exercises, at varying levels of difficulty, give readers practice in working with the ideas presented here.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 1999

Количество страниц: 386

Добавлена в каталог: 09.12.2006

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Предметный указатель

Inner regular measure      212
Integrable function      53
Integrable function, extended      86
Integrable function, locally      95
Integrable function, weakly      179
Integral of a complex function      53
Integral of a nonnegative function      50
Integral of a real function      53
Integral of a simple function      49
Integral, Bochner      179
Integral, Daniell      81
Integral, fractional      77
Integral, Henstock — Kurzweil      82
Integral, Lebesgue      56
Integral, Lebesgue — Stieltjes      107
Integral, Riemann      57
Interior      13 114
Invariant set      355
Inverse      4
Inverse image      3
Invertible linear map      154
Isometry      154
Isomorphism, Borel      83
Isomorphism, linear      154
Isomorphism, order      5
Isomorphism, unitary      176
Jensen's inequality      109
Joint distribution      315
Jordan content      72
Jordan decomposition of a function      103
Jordan decomposition of a signed measure      87
Jordan decomposition theorem      87
Kernel of a closed set      142
Kolmogorov's inequality      322
Krein extension theorem      161
Laplacian      273
Lattice of functions      139
Law of Large Numbers, strong      322—323
Law of large numbers, weak      321
Law of the iterated logarithm      336
LCH space      131
Lebesgue decomposition      91
Lebesgue Differentiation Theorem      98
Lebesgue integral      56
Lebesgue measurable function      44
Lebesgue measurable set      37 70
Lebesgue measure      37 70
Lebesgue set      97
Lebesgue — Radon — Nikodym theorem      90 93
Lebesgue — Stieltjes integral      107
Lebesgue — Stieltjes measure      35
Left continuous function      12
Left-invariant measure      341
Lemma, Borel — Cantelli      321
Lemma, Fatou's      52
Lemma, monotone class      66
Lemma, Riemann — Lebesgue      249
Lemma, three lines      200
Lemma, Urysohn's      122 131 245
Lemma, Weyl's      308
Lemma, Zorn's      5
Limit inferior      2 11
Limit of a net      126
Limit superior      2 11
Linear functional      157
Linear functional, positive      211
Linear ordering      5
Liouville's theorem      300
Lipschitz continuity      108
Localized Sobolev space      306
Locally compact group      341
Locally compact space      131
Locally convex space      165
Locally finite cover      135
Locally integrable function      95
Locally measurable set      28
Locally null set      192
Lower bound      5
Lower semicontinuous function      218
LSC function      218
Lusin's theorem      64 217
MAP      3
Mapping      3
Marcinkiewicz interpolation theorem      202
Maximal element      5
Maximal function      96 246
Maximal theorem      96
Meager set      161
Mean      314—315
Mean ergodic theorem      178
Measurable function      44
Measurable mapping      43
Measurable set      25
Measurable set with respect to an outer measure      29
Measurable set, Lebesgue      37 70
Measurable set, locally      28
Measurable space      25
Measure      24
Measure space      25
Measure, $\sigma$ -finite      25
Measure, Borel      33
Measure, complete      26
Measure, complex      93
Measure, continuous      106
Measure, counting      25
Measure, decomposable      92
Measure, dicrete      106
Measure, Dirac      25
Measure, finitely additive      25
Measure, Hausdorff      350
Measure, inner      32
Measure, inner regular      212
Measure, Lebesgue      37 70
Measure, Lebesgue — Stieltjes      35
Measure, outer      28
Measure, outer regular      212
Measure, positive      85
Measure, Radon      212
Measure, regular      99 212
Measure, semifinite      25
Measure, signed      85
Measure, singular      87
Measure, smooth      361
Metric      13
Metric outer measure      349
Metric space      13
Minimal element      5
Minkowski's inequality      183
Minkowski's inequality for integrals      194
Modular function      346
Moment convergence theorem      320
Monotone class      65
Monotone class lemma      66
Monotone Convergence Theorem      50
Monotone function      12
Monotonicity of measures      25
Multi-index      236
Mutually singular measures      87
Negative part of a function      46
Negative set      86
Negative variation of a function      103
Negative variation of a signed measure      87
Neighborhood      114
Neighborhood base      114
Net      125
Norm      152
Norm operator      154
Norm topology      152
Norm,       181 184
Norm, product      153

Norm, quotient      153
Norm, uniform      121
Normal distribution      325
Normal number      330
Normal space      117
Normed linear space      152
Normed vector space      152
Nowhere dense set      13 114
Null set      26 86
Null set, locally      192
One-point compactification      132
Open map      162
Open mapping theorem      162
Open set      12—13 114
Operator norm      154
Order isomorphism      5
Order topology      118
Ordinal      10
Orientable manifold      362
Orientation      362
Orthogonal projection      177
Orthogonal set      173
Orthonormal basis      176
Orthonormal set      175
Outer measure      28
Outer measure, metric      349
Outer regular measure      212
Paracompact space      135
Parallelogram law      173
Parametrization      352
Parseval's identity      175
Partial ordering      4
Partition of an interval      56
Partition of unity      134
Partition, tagged      82
Periodic distribution      297
Periodic function      238
Plancherel theorem      252
Point mass      25
Pointwise bounded family      137
Poisson distribution      320
Poisson kernel      260 262
Poisson summation formula      254
Polar coordinates      78
Polar decomposition      46
Positive definite function      272
Positive linear functional      211
Positive measure      85
Positive part of a function      46
Positive set      86
Positive variation of a function      103
Positive variation of a signed measure      87
Pre-Hilbert space      172
Precompact set      128
Predecesor      9
Premeasure      30
Principal symbol      306
Probability measure      313
Product $\sigma$ -algebra      22
Product measure      64
Product metric      13
Product norm      153
Product topology      120
Projection      4
Projection, orthogonal      177
Proper map      135
Pythagorean Theorem      173
Quotient norm      153
Quotient space      153
Quotient topology      124
Radon measure      212
Radon measure, complex      222
Radon product      227
Radon — Nikodym derivative      91
Radon — Nikodym theorem      91
Random variable      314
RANGE      4
Real-analytic function      263
rectangle      64
Refinement of a cover      135
Reflexive space      159
Regular measure      99 212
Regular space      117
Relation      3
Relative topology      114
Rellich's theorem      305
Residual set      161
Reverse inclusion      125
Riemann integrable function      57
Riemann integral      57
Riemann — Lebesgue lemma      249
Riemannian volume density      362
Riesz representation theorem      212 223
Riesz — Thorin interpolation theorem      200
Right continuous function      12
Right-invariant measure      341
Ring of sets      24
Sample mean      325
Sample space      314
Sample variance      325
Sampling theorem      255
Saturated measure      28
Saturation of a measure      28
Scalar product      171
Schroder — Bernstein theorem      7
Schwartz space      236
Schwarz inequality      172
Second category      161
Second countable space      116
Section of a set or function      65
Semi norm      151
Semifinite measure      25
Semifinite part      27
Separable space      14 116
Separating set      359
Separation of points      139
Separation of points and closed sets      143
SEQUENCE      4
Sequentially compact space      130
Shannon's Theorem      324
Shrink nicely      98
Sides of a rectangle      70
Sierpinski gasket      356
Signed measure      85
Similitude      355
Simple function      46
Singular measure      87
Slowly increasing function      294
Smooth measure      361
Snowflake curve      356
Sobolev embedding theorem      303 308
Sobolev space      301
Sobolev space, localized      306
Standard deviation      314
Standard normal distribution      325
Standard representation of a simple function      46
Stirling's formula      327
Stone — Cech compactification      144
Stone — Weierstrass theorem      139 141
Strong Law of Large Numbers      322—323
Strong operator topology      169
Strong type      202
Stronger topology      114
Subadditivity      25
Subbase for a topology      114
Sublinear functional      157
Sublinear map      202
Submanifold      351
Subnet      126
Subordination      134

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