Bear H.S. — A Primer of Lebesgue Integration :: Электронная библиотека попечительского совета мехмата МГУ

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Bear H.S. — A Primer of Lebesgue Integration

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Название: A Primer of Lebesgue Integration

Автор: Bear H.S.

Аннотация:

This successful text offers a reader-friendly approach to Lebesgue integration. It is designed for advanced undergraduates, beginning graduate students, or advanced readers who may have forgotten one or two details from their real analysis courses.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 2001

Количество страниц: 164

Добавлена в каталог: 13.12.2009

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Предметный указатель

$L^{2}$       152
$R_{\sigma}$ , $R_{\sigma \delta}$       141
$\ell^{2}$       149 152
$\mathbb{Q}$ (the rationals)      21 25
$\sigma$ -algebra      35 107
$\sigma$ -finite      101 110
Absolute value of a vector      150
Absolutely continuous      129
Absolutely convergent      18 154
Admissible function      63 118
Admissible partition      63 118
Algebra generated by a family      138
Algebra of sets      136
Almost everywhere (a.e.)      49
Axiom of Choice      37
Basket of numbers      17
Bessel's inequality      158
Bounded convergence theorem      58 123
Cantor set      39 60
Caratheodory criterion      30
Cauchy net      18
Cauchy's inequality      151
Characteristic function      46
Choice function      12 53
Compact set      22
Complete measure      108 110
Complete normed space      154
Convergent net      10
Convex function      153
Countable additivity      31
Countable partition      62
Countable subadditivity      24 87
Countable subadditivity for signed measures      111
Counting measure      105 108
Covering of a set      22
Cross section      98
Differentiation under the integral sign      71
Dini derivates      77
Directed set      10
Dirichlet problem      81
Distance in $\mathbb{R}^{n}$       151
Dominated Convergence Theorem      68 123
Double integral      135
Dyadic interval      86
Dyadic square      86
Egoroff's theorem      58 122
Fatou's lemma      68 123 124
Fourier coefficients      157
Fourier series      157
Fubini's theorem      101 145
Fundamental theorem of calculus      73
Hahn decomposition      114
Harmonic function      81
Heine — Borel theorem      22
Improper integral      6
Inner measure ( $m_{*}$ )      41
Inner product in $L^{2}$       152
Integrable function, Lebesgue      45 118
Integrable function, Riemann      2
Integral, improper Riemann      6
Integral, Lebesgue      45
Integral, Riemann      2
Iterated integral      135

Jordan decomposition      115
L(f,P)      2
Lebesgue (outer) measure      21 22 85
Lebesgue (outer) measure, in the plane      85
Lebesgue dominated convergence theorem      68 123
Lebesgue integrable function      45
Lebesgue singular function      75
Linear space      152
Little boy      17
Lower sum, upper sum      2
m*, $m_{*}$       28 41
Measurable function      46 117
Measurable set      27 88 140
Measure      21 22
Measure space      107
Measure, complete      109
Metric      152
Minkowski's inequality      151
Monotone Convergence Theorem      69 124
Monotonicity of measures      23 167
Negative set      111
Net      10
Nonmeasurable set      37
Norm      19 153 156
Null set      109 112
Outer measure (m*)      28
Partition      1 43
Point mass      108
Poisson kernel      82
Positive set      111
R(f,P,c)      13
Radon — Nikodym derivative      132
Radon — Nikodym theorem      130
Rational numbers      21 25
Rectangles      85 136 137
refinement      3 43
Regular measure      91
Riemann integrable      2 13 60
Riemann integral      1
Riemann sum      12 53
Riesz — Fischer theorem      155 159
Scalar multiplication      149
Scalar product      150
Section of a set      141
Signed measure      111
Simple function      46 119
Singular measures      114 132
Step function      5
Subadditive      24
Summable      17
Symmetric difference      39
Tonelli's theorem      101 147
Total length of a covering      22
Total variation of a measure      115
Trigonometric series      156
U(f,P)      2
Unordered sum      17
Upper and lower sums      2
Upper and lower sums, for Lebesgue integral      43
Vector space      149
Vitali covering      75
Vitali's theorem      75
Zorn's lemma      37

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