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| Bear H.S. — A Primer of Lebesgue Integration |
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| Предметный указатель |
 152
 ,  141
 149 152
 (the rationals) 21 25
 -algebra 35 107
-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  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 ( ) 41
Inner product in 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*, 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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