Real analysis / [by] H. L. Royden.
Editor: New York : Macmillan, [1968]Edición: 2nd edDescripción: xii, 349 p. ; 24 cmOtra clasificación: 26-01 (26A24 28-01 28A25 28C05 46-01 46B07 46B22)Prologue to the Student [1] 1 Set Theory 1 Introduction, [5] 2 Functions, [8] 3 Unions, intersections, and complements, [11] 4 Algebras of sets, [16] 5 The axiom of choice and infinite direct products, [18] 6 Countable sets, [19] 7 Relations and equivalences, [22] 8 Partial orderings and the maximal principle, [23] 9 Well ordering and the countable ordinals, [24] Part One □ Theory of Functions of a Real Variable 2 The Real Number System [29] 1 Axioms for the real numbers, [29] 2 The natural and rational numbers as subsets of R, [32] 3 The extended real numbers, [34] 4 Sequences of real numbers, [35] 5 Open and closed sets of real numbers, [38] 6 Continuous functions, [44] 7 Borel sets, [50] 3 Lebesgue Measure [52] 1 Introduction, [52] 2 Outer measure, [54] 3 Measurable sets and Lebesgue measure, [56] *4 A nonmeasurable set, [63] 5 Measurable functions, [65] 6 Littlewood's three principles, [71] 4 The Lebesgue Integral [73] 1 The Riemann integral, [73] 2 The Lebesgue integral of a bounded function over a set of finite measure, [75] 3 The integral of a nonnegative function, [82] 4 The general Lebesgue integral, [86] *5 Convergence in measure, [91] 5 Differentiation and Integration [94] 1 Differentiation of monotone functions, [94] 2 Functions of bounded variation, [98] 3 Differentiation of an integral, [101] 4 Absolute continuity, [104] *5 Convex functions, [108] 6 The Classical Banach Spaces [111] 1 The Lp spaces, [111] 2 The Holder and Minkowski inequalities, [112] 3 Convergence and completeness, [115] 4 Bounded linear functionals on the Lp spaces, [119] Part Two □ Abstract Spaces 7 Metric Spaces [127] 1 Introduction, [127] 2 Open and closed sets, [129] 3 Continuous functions and homeomorphisms, [131] 4 Convergence and completeness, [133] 5 Uniform continuity and uniformity, [135] 6 Subspaces, [137] 7 Baire category, [139] Indicates sections peripheral to the principal line of argument. 8 Topological Spaces [142] 1 Fundamental notions, [142] 2 Bases and countability, [145] 3 The separation axioms and continuous real-valued functions, [147] 4 Product spaces, [150] 5 Connectedness, [150] *6 Absolute Ʒ؏’S, [154] *7 Nets, [155] 9 Compact Spaces [157] 1 Basic properties, [157] 2 Countable compactness and the Bolzano-Weierstrassproperty, [159] 3 Compact metric spaces, [163] 4 Products of compact spaces, [165] 5 Locally compact spaces, [168] *6 The Stone-Čech compactification, [170] 7 The Stone-Weierstrass theorem, [171] *8 The Ascoli theorem, [177] 10 Banach Spaces [181] 1 Introduction, [181] 2 Linear operators, [184] 3 Linear functionals and the Hahn-Banach theorem, [186] 4 The closed graph theorem, [193] *5 Topological vector spaces, [197] *6 Weak topologies, [200] *7 Convexity, [203] 8 Hilbert space, [210] Part Three □ General Measure and Integration Theory 11 Measure and Integration [217] 1 Measure spaces, [217] 2 Measurable functions, [223] 3 Integration, [225] *4 General convergence theorems, [231] 5 Signed measures, [232] 6 The Radon-Nikodym theorem, [238] 7 The Lp spaces, [243] 12 Measure and Outer Measure [250] 1 Outer measure and measurability, [250] 2 The extension theorem, [253] *3 The Lebesgue-Stieltjes integral, [261] 4 Product measures, [264] *5 Inner measure, [274] *6 Extension by sets of measure zero, [281] *7 Caratheodory outer measure, [283] 13 The Daniell Integral [286] 1 Introduction, [286] 2 The extension theorem, [288] 3 Uniqueness, [294] 4 Measurability and measure, [295] 14 Measure and Topology [301] 1 Baire sets and Borel sets, [301] 2 Positive linear functionals and Baire measures, [304] 3 Bounded linear functionals on C(X), [308] *4 The Borel extension of a measure, [313] 15 Mappings of Measure Spaces [317] 1 Point mappings and set mappings, [317] 2 Measure algebras, [319] 3 Borel equivalences, [324] 4 Set mappings and point mappings on complete metric spaces, [328] 5 The isometries of Lp, [331] Epilogue [335] Bibliography [337] Index of Symbols [339] Subject Index [341]
| Item type | Home library | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
|---|---|---|---|---|---|---|---|
Libros
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Instituto de Matemática, CONICET-UNS | 26 R888-2 (Browse shelf) | Available | A-8040 |
Bibliografía: p. 337-338.
Prologue to the Student [1] --
1 Set Theory --
1 Introduction, [5] --
2 Functions, [8] --
3 Unions, intersections, and complements, [11] --
4 Algebras of sets, [16] --
5 The axiom of choice and infinite direct products, [18] --
6 Countable sets, [19] --
7 Relations and equivalences, [22] --
8 Partial orderings and the maximal principle, [23] --
9 Well ordering and the countable ordinals, [24] --
Part One □ Theory of Functions of a Real Variable --
2 The Real Number System [29] --
1 Axioms for the real numbers, [29] --
2 The natural and rational numbers as subsets of R, [32] --
3 The extended real numbers, [34] --
4 Sequences of real numbers, [35] --
5 Open and closed sets of real numbers, [38] --
6 Continuous functions, [44] --
7 Borel sets, [50] --
3 Lebesgue Measure [52] --
1 Introduction, [52] --
2 Outer measure, [54] --
3 Measurable sets and Lebesgue measure, [56] --
*4 A nonmeasurable set, [63] --
5 Measurable functions, [65] --
6 Littlewood's three principles, [71] --
4 The Lebesgue Integral [73] --
1 The Riemann integral, [73] --
2 The Lebesgue integral of a bounded function over a set of finite measure, [75] --
3 The integral of a nonnegative function, [82] --
4 The general Lebesgue integral, [86] --
*5 Convergence in measure, [91] --
5 Differentiation and Integration [94] --
1 Differentiation of monotone functions, [94] --
2 Functions of bounded variation, [98] --
3 Differentiation of an integral, [101] --
4 Absolute continuity, [104] --
*5 Convex functions, [108] --
6 The Classical Banach Spaces [111] --
1 The Lp spaces, [111] --
2 The Holder and Minkowski inequalities, [112] --
3 Convergence and completeness, [115] --
4 Bounded linear functionals on the Lp spaces, [119] --
Part Two □ Abstract Spaces --
7 Metric Spaces [127] --
1 Introduction, [127] --
2 Open and closed sets, [129] --
3 Continuous functions and homeomorphisms, [131] --
4 Convergence and completeness, [133] --
5 Uniform continuity and uniformity, [135] --
6 Subspaces, [137] --
7 Baire category, [139] --
Indicates sections peripheral to the principal line of argument. --
8 Topological Spaces [142] --
1 Fundamental notions, [142] --
2 Bases and countability, [145] --
3 The separation axioms and continuous real-valued functions, [147] --
4 Product spaces, [150] --
5 Connectedness, [150] --
*6 Absolute Ʒ؏’S, [154] --
*7 Nets, [155] --
9 Compact Spaces [157] --
1 Basic properties, [157] --
2 Countable compactness and the Bolzano-Weierstrassproperty, [159] --
3 Compact metric spaces, [163] --
4 Products of compact spaces, [165] --
5 Locally compact spaces, [168] --
*6 The Stone-Čech compactification, [170] --
7 The Stone-Weierstrass theorem, [171] --
*8 The Ascoli theorem, [177] --
10 Banach Spaces [181] --
1 Introduction, [181] --
2 Linear operators, [184] --
3 Linear functionals and the Hahn-Banach theorem, [186] --
4 The closed graph theorem, [193] --
*5 Topological vector spaces, [197] --
*6 Weak topologies, [200] --
*7 Convexity, [203] --
8 Hilbert space, [210] --
Part Three □ General Measure and Integration Theory --
11 Measure and Integration [217] --
1 Measure spaces, [217] --
2 Measurable functions, [223] --
3 Integration, [225] --
*4 General convergence theorems, [231] --
5 Signed measures, [232] --
6 The Radon-Nikodym theorem, [238] --
7 The Lp spaces, [243] --
12 Measure and Outer Measure [250] --
1 Outer measure and measurability, [250] --
2 The extension theorem, [253] --
*3 The Lebesgue-Stieltjes integral, [261] --
4 Product measures, [264] --
*5 Inner measure, [274] --
*6 Extension by sets of measure zero, [281] --
*7 Caratheodory outer measure, [283] --
13 The Daniell Integral [286] --
1 Introduction, [286] --
2 The extension theorem, [288] --
3 Uniqueness, [294] --
4 Measurability and measure, [295] --
14 Measure and Topology [301] --
1 Baire sets and Borel sets, [301] --
2 Positive linear functionals and Baire measures, [304] --
3 Bounded linear functionals on C(X), [308] --
*4 The Borel extension of a measure, [313] --
15 Mappings of Measure Spaces [317] --
1 Point mappings and set mappings, [317] --
2 Measure algebras, [319] --
3 Borel equivalences, [324] --
4 Set mappings and point mappings on complete metric spaces, [328] --
5 The isometries of Lp, [331] --
Epilogue [335] --
Bibliography [337] --
Index of Symbols [339] --
Subject Index [341] --
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