Priestley, H. A. (Hilary A.)
Introduction to integration / H. A. Priestley.
— Oxford : Clarendon Press ; New York : Oxford University Press, 1997. x, 306 : il. ; 24 cm.
Incluye referencias bibliográficas (p. [295]) e índices.
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.
ISBN 0198501242 (hbk). — ISBN 0198501234 (pbk)
|