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A course of higher mathematics. Volume V, Integration and functional analysis /
International Series of Monographs in Pure and Applied Mathematics, Volume 62: A Course of Higher Mathematics, V: Integration and Functional Analysis focuses on the theory of functions. The book first discusses the Stieltjes integral. Concerns include sets and their powers, Darboux sums, improper St...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Ruso |
| Publicado: |
Oxford :
Pergamon Press,
1964.
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| Colección: | International series of monographs in pure and applied mathematics ;
62. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Higher Mathematics; Copyright Page ; Table of Contents; INTRODUCTION; PREFACE; CHAPTER 1. THE STIELTJES INTEGRAL; 1. Sets and their powers; 2. The Stieltjes integral and its basic properties; 3. Darboux sums; 4. The Stieltjes integral of a continuous function; 5� The improper Stieltjes integral; 6. Jump functions; 7. Physical interpretation; 8. Functions of bounded variation; 9� An integrating function of bounded variation; 10. Existence of the Stieltjes integral; 11. Passage to the limit in the Stieltjes integral; 12. Helly's theorem; 13. Selection principle.
- 14. Space of continuoue fonctione15. General form of the functional in space C; 16. Linear operators in C; 17� Functions of an interval; 18. The general Stieltjes integral; 19. Properties of the (general) Stieltjes integral; 20. The existence of the general Stieltjes integral; 21� Functions of a two-dimensional interval; 22. Passage to point functions; 23. The Stieltjes integral on a plane; 24. Functions of bounded variation on the plane; 25. The space of continuous functions of several variables; 26. The Fourier-Stieltjes integral; 27. Inversion formula; 28. ConvoIution theorem.
- 44. The limit of a measurable function45. The C properly; 46. Piecewise constant functions; 47. Class B ; 3. The Lebesgue integral; 48. The integral of a bounded function; 49. Properties of the integral; 50� The integral of a non-negative unbounded function; 51. Properties of the integral; 52� Functions of any sign; 53. Complex summable functions; 54. Passage to the limit under the integral sign; 55� The class L2; 56. Convergence in the mean; 57. Hilbert function space; 58� Orthogonal systems of functions; 59. The space l2; 60. Lineals in L2; 61. Examples of closed systems.
- 62. The Holder and Minhkoskii inequalities63. Integral over a set of infinite measure; 64. The class L2 on a set of infinite measure; 65� An integrating function of bounded variation; 66. The reduction of multiple integrals; 67� The case of the characteristic function; 68� Fubini's theorem; 69. Change of the order of integration; 70. Continuity in the mean; 71. Mean functions; CHAPTER 3. SET FUNCTIONS. ABSOLUTE CONTINUITY GENERALIZATION OF THE INTEGRAL; 72. Additive set functions; 73. Siogular function; 74� The case of one variable; 75. Absolutely continuous set functions; 76. Example.