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Introduction to Integration

by Priestley, Hilary A. A Priestley, H. A.

Introduction to Integration cover
  • ISBN: 9780198501237
  • ISBN10: 0198501234

Introduction to Integration

by Priestley, Hilary A. A Priestley, H. A.

  • Binding: Paperback
  • Publisher: Oxford University Press
  • Publish date: 12/01/1997
  • ISBN: 9780198501237
  • ISBN10: 0198501234
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Description: 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 on 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. Fourier transforms 34. Integration in probability theory Appendix I Appendix II Bibliography Notation index Subject index
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