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A primer of real functions /
"This is a revised, updated, and augmented edition of a classic Carus monograph with a new chapter on integration and its applications. Earlier editions covered sets, metric spaces, continuous functions, and differentiable functions. To that, this edition adds sections on measurable sets and fu...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
[Washington, D.C.] :
Mathematical Association of America,
©1996.
|
| Edición: | 4th ed. / |
| Colección: | Carus mathematical monographs ;
no. 13. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface to the fourth edition
- Preface to the third edition
- [ch.] 1. Sets
- 1. Sets
- 2. Sets of real numbers
- 3. Countable and uncountable sets
- 4. Metric spaces
- 5. Open and closed sets
- 6. Dense and nowhere dense sets
- 7. Compactness
- 8. Convergence and completeness
- 9. Nested sets and Baire's theorem
- 10. Some applications of Baire's theorem
- 11. Sets of measure zero
- [c.h.] 2. Functions
- 12. Functions
- 13. Continuous functions
- 14. Properties of continuous functions
- 15. Upper and lower limits
- 16. Sequences of functions
- 17. Uniform convergence
- 18. Point wise limits on continuous functions
- 19. Approximations to continuous functions
- 20. Linear functions
- 21. Derivaties
- 22. Monotonic functions
- 23. Convex functions
- 24. Infinitely differentiable functions
- [ch.] 3. Integration
- 25. Lebesgue measure
- 26. Measurable functions
- 27. Definition of the Lebesgue integral
- 28. Properties of Lebesgue integrals
- 29. Applications of the Lebesgue integral
- 30. Stieltjes integrals
- 31. Applications of the Stieltjes integral
- 32. Partial sums of infinite series
- Answers to exercises
- Index.