Introduction to integration /
Guardado en:
| Autor Principal: | |
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| Formato: | Libro |
| Idioma: | English |
| Publicado: |
Oxford : New York :
Clarendon Press ; Oxford University Press,
1997.
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| Materias: | |
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Tabla de Contenidos:
- 1. Setting the scene
- 2. Preliminaries
- 3. Intervals and step functions
- 4. Integrals of step functions
- 5. Continuous functions on compact intervals
- 6. Techniques of Integration I
- 7. Approximations
- 8 Uniform convergence and power series
- 9. Building foundations
- 10. Null sets
- 11. Linc functions
- 12. The space L of integrable functions
- 13 Non-integrable functions
- 14. Convergence Theorems: MCT and DCT
- 15 Recognizing integrable functions I
- 16. Techniques of integration II
- 17. Sums and integrals
- 18. Recognizing integrable functions II
- 19. The Continuous DCT
- 20. Differentiation of integrals
- 21. Measurable functions
- 22. Measurable sets
- 23. The character of integrable functions
- 24. Integration vs. differentiation
- 25. Integrable functions of Rk
- 26. Fubini's Theorem and Tonelli's Theorem
- 27. Transformations of Rk
- 28. The spaces L1, L2 and Lp
- 29. Fourier series: pointwise convergence
- 30. Fourier series: convergence re-assessed
- 31. L2-spaces: orthogonal sequences
- 32. L2-spaces as Hilbert spaces
- 33. The Fourier transform
- 34. Integration in probability theory.