The integrals of Lebesgue, Denjoy, Perron, and Henstock /
Suppose that f : [a,b] -> R is differentiable at each point of [a,b]. Is f' integrable on [a,b]? The answer to this question depends on the integral that is used. For example, the answer is no for the Riemann and Lebesgue integrals. In this century, three integrations processes have been dev...
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| Autor Principal: | |
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| Formato: | Libro |
| Idioma: | English |
| Publicado: |
Providence, R.I. :
American Mathematical Society,
c1994.
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| Series: | Graduate studies in mathematics,
v. 4 |
| Materias: | |
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Tabla de Contenidos:
- Capítulos: 1. Lebesgue measure
- 2. Measurable functions
- 3. The Lebesgue integral
- 4. Bounded variation and absolute continuity
- 5. Darboux and Baire class one functions
- 6. Functions of generalized bounded variation
- 7. The Denjoy integral
- 8. The Perron integral
- 9. The Henstock integral
- 10. The McShane integral
- 11. Equivalence of integrals
- 12. Integration by parts
- 13. Convergence theorems
- 14. Approximate derivatives
- 15. The Khintchine integral
- 16. The approximately continuous Henstock integral
- 17. The approximately continuous Perron integral.