Introduction to integration
H. A. Priestley.
Oxford : Clarendon Press ; New York : Oxford University Press, 1997.
x, 306 : ilustraciones ; 24 cm.
ISBN: 0198501242 (hbk), 0198501234 (pbk)
Incluye referencias bibliográficas (p. [295]) e índices.
Reseña: MathSciNet, 99d:28001
Contenido
- 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.
