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| Aliprantis C. — Principles of real analysis |
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| Предметный указатель |
Number, algebraic 13
Number, cardinal 12
Number, Lebesgue 50
Number, negative 15
Number, positive 15
Odd polynomial 90
One-to-one function 5
Onto function 5
Open ball 35 366
Open cover 48
Open mapping 52
Open mapping theorem 232
Open set 35 58
Open unit ball 220
Open, mapping 52
Operator 224
Operator norm 225
Operator, adjoint 297
Operator, averaging 253
Operator, bounded 225
Operator, compact 226
Operator, differential 225 227
Operator, inner product preserving 304
Operator, integral 226
Operator, Laplace 250
Operator, linear 224
Operator, norm preserving 304
Operator, positive 249
Operator, projection 235
Operator, rank-one 242
Operator, symmetric 287
Operator, unbounded 225
Order axioms 15
Order bounded linear functional 244
Order bounded set 244
Order complete vector lattice 252
Order continuity of the integral 129 164
Order dual 244
Order, partial 7
Ordered pair 6
Ordered vector space 66 242
Ordinate set of function 215
Orthogonal complement 287 291
Orthogonal measures 339
Orthogonal set 282
Orthogonal set, complete 293
Orthogonal vectors 282
Orthonormal basis 298
Orthonormal set 282
Orthonormal set, complete 298
Oscillation 372
Oscillation of function 61
Outer measure 103
Outer measure generated by a measure 107
Outer measure, induced by a positive functional 353
Output 5
p-adic representation of number 32
Pairwise disjoint family 4
Parallelogram law 279
Parseval's identity 298
Parseval, Marc-Antoine C. (1755-1836) 298
Partial derivative 193
Partial order 7
Partially ordered set 8
Partially ordered vector space 242
Partition 186
Partition of interval 178 376
Partition of set 7
Partition of unity 86
Partition, finer 178
Perfectly normal space 87
Period of function 307
Periodic function 307
Permutation of  30
Plus infinity 29
Point of a set 2
Point, accumulation 37 59
Point, boundary 38 59
Point, closure 36 59
Point, cluster 23
Point, density 371
Point, fixed 55
Point, interior 35 59
Point, isolated 56
Point, Lebesgue 382
Point, limit 23
Pointwise bounded set 228
Pointwise convergence 68
Pointwise finite cover 56
Pointwise limit 68
Polar coordinate transformation 394
Polar coordinates 394
Polynomial, even 90
Polynomial, Hermite 304
Polynomial, odd 90
Positive cone 242
Positive definite matrix 287
Positive linear functional 244
Positive number 15
Positive operator 249
Positive part of vector 67 243
Positive set 330
Positive variation of a signed measure 332
Positive vector 67 242
Power set 4
Principle, condensation of singularities 230
Principle, mathematical induction 10
Principle, uniform boundedness 229
Principle, well ordering 10
Product  -algebra 154
Product measure 204
Product semiring 154 204
Product, cartesian 6
Product, inner 276
Projection 235
Proper subset 2
Property, Archimedean 17
Property, eventually true 22
Property, finite intersection 55
Property, topological 55
Pythagoras of Samos (ca 580-500 BC) 282
Pythagorean Theorem 282
Quotient topology 65
Radon — Nikodym derivative 344
Radon — Nikodym theorem 342
Radon, Johann (1887-1956) 342
Range of function 5
Rank-one operator 242
Rearrangement invariant series 30
Reciprocal of real number 20
rectangle 204
Reflexive Banach space 239
Reflexivity 7 66
Regular Borel measure 136 352
Regular Borel signed measure 362
Relation 7
Relation, a.e. 120
Relation, binary 7
Relation, equivalence 7
Relative topology 58
Representing measure 352
Restriction semiring 97
Riemann integrable function 180 187
Riemann integral 180 187
Riemann integral, improper 190
Riemann integral, lower 179 186
Riemann integral, upper 179 187
Riemann sum 181
Riemann's criterion 180
Riemann, Bernhard G.F. (1826-1866) 177 180 202
| Riesz representation theorem 355
Riesz space 242
Riesz, Frigyes (1880-1956) 242 244 258 292 344 355
Right translate of function 362
Right-invariant functional 363
Ring of sets 96 149
Root of real number 19
Schmidt, Erhard (1876-1959) 284
Schroeder — Bernstein theorem 12
Schroeder, Ernst (1841-1902) 12
Schwarz, Hermann A. (1843-1921) 256 278
Second dual of Banach space 239
Section of set 154
Segment 9
Selection of points 181
Semiring of sets 94
Semiring, product 154 204
Semiring, restriction 97
Separable metric space 54
Separately measurable function 155
Separation by a continuous function 80
Separation by open sets 80
Separation of points by a family 87
SEQUENCE 6
Sequence convergent 22 37
Sequence convergent to  29
Sequence of averages 27
Sequence of functions, decreasing 70
Sequence of functions, increasing 70
Sequence of functions, monotone 70
Sequence, Cauchy 26 39
Sequence, constant 23
Sequence, convergent 22 37 60
Sequence, convergent in mean 202
Sequence, convergent to 29
Sequence, decreasing 22
Sequence, increasing 22
Sequence, monotone 22
Series, absolutely summable 223
Series, alternating 33
Series, convergent in Banach space 223
Series, double 30
Series, Fourier 309
Series, harmonic 33
Series, rearrangement invariant 30
Series, unconditionally convergent 33
Series, uniformly convergent 71
Set 2
Set difference 2
Set function 98
Set function, -subadditive 103
Set inclusion 2
Set intersection 2 3
Set of first category 43 59
Set union 2 3
Set,  -Cantor 141
Set, -compact 357
Set, -finite 116 175
Set, atom 120
Set, balanced 224
Set, Borel 97
Set, bounded 16
Set, bounded from above 16
Set, bounded from below 16
Set, Cantor 41 140
Set, circled 224
Set, clopen 65
Set, closed 35 58
Set, co-meager 48
Set, compact 49 62
Set, connected 47
Set, convex 224
Set, countable 9
Set, dense 37 59
Set, derived 37 59
Set, empty 2
Set, equality 2
Set, equicontinuous 75
Set, finite 9
Set, index 3
Set, infinite 9
Set, meager 43 59
Set, measurable 103 112 151
Set, negative 330
Set, norm bounded 218
Set, nowhere dense 41 59
Set, null 104
Set, open 35 58
Set, order bounded 244
Set, ordinate 215
Set, orthogonal 282
Set, orthonormal 282 298
Set, partially ordered 8
Set, pointwise bounded 228
Set, positive 330
Set, power 4
Set, symmetric 224
Set, totally ordered 8
Set, uncountable 9
Set, void 2
Sets, equivalent 9
Signed measure 329
Signed measure, -finite 332
Signed measure, Borel 362
Signed measure, finite 332
Signed measure, regular Borel 362
Simple function 127
Singleton 2
Singular measures 339
Space, Baire 43
Space, Banach 218
Space, function 68
Space, Hausdorff 60
Space, Hilbert 288
Space, measurable 151
Space, measure 99
Space, metric 34
Space, Riesz 242
Space, topological 58
Spherical coordinate transformation 396
Spherical coordinates 396
Square summable function 305
Standard representation of simple function 127
Steinhaus, Hugo (1887-1972) 144 229
Step function 127
Stieltjes, Thomas J. (1856-1894) 379
Stone — Weierstrass theorem 88 89
Stone, Marshall H. (1903-1989) 88 89
Strictly decreasing function 372
Strictly increasing function 372
Strictly monotone function 372
Subcover of set 48
Sublinear mapping 236
Subsequence 6
Subset of set 2
Subset, proper 2
Subtraction 20
Sum of arbitrary numbers 283
Sum, Riemann 181
Sup norm 69 219
Support of function 85 201
Support of measure 263
Supremum 16
Supremum, essential 260
Surjective function 5
Symmetric difference 3
Symmetric matrix 287
Symmetric operator 287
Symmetric set 224
Symmetry 7
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