Elements of the theory of functions and functional analysis / by A.N. Kolmogorov and S.V. Fomin. Translated from the 1st Russian ed. by Leo F. Boron.
Idioma: Inglés Lenguaje original: Ruso Editor: Rochester, N.Y. : Graylock Press, 1957-Descripción: v. : il. ; 24 cmTítulos uniformes: Elementy teorii funktsii i funktsional'nogo analiza. Inglés Tema(s): Functions of real variables | Functional analysisOtra clasificación: 46-01 (28-01 47-01)v. 1. Metric and normed spacesv. 2. Measure. The Lebesgue integral. Hilbert space. Preface vii Translator’s Note ix CHAPTER I Fundamentals of Set Theory 1. The Concept of Set. Operations on Sets [1] 2. Finite and Infinite Sets. Denumerability [3] 3. Equivalence of Sets [6] 4. The Nondenumerability of the Set of Real Numbers [8] 5. The Concept of Cardinal Number [9] 6. Partition into Classes [11] 7. Mappings of Sets. General Concept of Function [13] CHAPTER II Metric Spaces 8. Definition and Examples of Metric Spaces [16] 9. Convergence of Sequences. Limit Points [23] 10. Open and Closed Sets.. . [26] 11. Open and Closed Sets on the Real Line [31] 12. Continuous Mappings. Homeomorphism. Isometry [33] 13. Complete Metric Spaces [36] 14. The Principle of Contraction Mappings and its Applications [43] 15. Applications of the Principle of Contraction Mappings in Analysis [46] 16. Compact Sets in Metric Spaces [51] 17. Arzelà’s Theorem and its Applications [53] 18. Compacta [57] 19. Real Functions in Metric Spaces [62] 20. Continuous Curves in Metric Spaces [66] CHAPTER III Normed Linear Spaces 21. Definition and Examples of Normed Linear Spaces [71] 22. Convex Sets in Normed Linear Spaces [74] 23. Linear Functionals [77] 24. The Conjugate Space [81] 25. Extension of Linear Functionals [86] 26. The Second Conjugate Space [88] 27. Weak Convergence [90] 28. Weak Convergence of Linear Functionals [92] 29. Linear Operators [95] ADDENDUM TO CHAPTER III Generalized Functions CHAPTER IV Linear Operator Equations 30. Spectrum of an Operator. Resolvents [110] 31. Completely Continuous Operators [112] 32. Linear Operator Equations. Fredholm’s Theorems [116] List of Symbols [122] List of Definitions [123] List of Theorems [123] Basic Literature [125] Index [127]
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 46 K81i (Browse shelf) | Vol. 1 | Available | A-2089 |
Vol. 2, translated by Hyman Kamel and Horace Komm, published in Albany.
v. 1. Metric and normed spaces -- v. 2. Measure. The Lebesgue integral. Hilbert space.
Preface vii --
Translator’s Note ix --
CHAPTER I --
Fundamentals of Set Theory --
1. The Concept of Set. Operations on Sets [1] --
2. Finite and Infinite Sets. Denumerability [3] --
3. Equivalence of Sets [6] --
4. The Nondenumerability of the Set of Real Numbers [8] --
5. The Concept of Cardinal Number [9] --
6. Partition into Classes [11] --
7. Mappings of Sets. General Concept of Function [13] --
CHAPTER II --
Metric Spaces --
8. Definition and Examples of Metric Spaces [16] --
9. Convergence of Sequences. Limit Points [23] --
10. Open and Closed Sets.. . [26] --
11. Open and Closed Sets on the Real Line [31] --
12. Continuous Mappings. Homeomorphism. Isometry [33] --
13. Complete Metric Spaces [36] --
14. The Principle of Contraction Mappings and its Applications [43] --
15. Applications of the Principle of Contraction Mappings in Analysis [46] --
16. Compact Sets in Metric Spaces [51] --
17. Arzelà’s Theorem and its Applications [53] --
18. Compacta [57] --
19. Real Functions in Metric Spaces [62] --
20. Continuous Curves in Metric Spaces [66] --
CHAPTER III --
Normed Linear Spaces --
21. Definition and Examples of Normed Linear Spaces [71] --
22. Convex Sets in Normed Linear Spaces [74] --
23. Linear Functionals [77] --
24. The Conjugate Space [81] --
25. Extension of Linear Functionals [86] --
26. The Second Conjugate Space [88] --
27. Weak Convergence [90] --
28. Weak Convergence of Linear Functionals [92] --
29. Linear Operators [95] --
ADDENDUM TO CHAPTER III --
Generalized Functions --
CHAPTER IV --
Linear Operator Equations --
30. Spectrum of an Operator. Resolvents [110] --
31. Completely Continuous Operators [112] --
32. Linear Operator Equations. Fredholm’s Theorems [116] --
List of Symbols [122] --
List of Definitions [123] --
List of Theorems [123] --
Basic Literature [125] --
Index [127] --
MR, 19,44d
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