Table of Contents

1. Setting the scene2. Preliminaries3. Intervals and step functions4. Integrals of step functions5. Continuous functions on compact intervals6. Techniques of Integration I7. Approximations8. Uniform convergence and power series9. Building foundations10. Null sets11. Linc functions12. The space L of integrable functions13. Non-integrable functions14. Convergence Theorems: MCT and DCT15. Recognizing integrable functions I16. Techniques of integration II17. Sums and integrals18. Recognizing integrable functions II19. The Continuous DCT20. Differentiation of integrals21. Measurable functions22. Measurable sets23. The character of integrable functions24. Integration vs. differentiation25. Integrable functions on Rk26. Fubini's Theorem and Tonelli's Theorem27. Transformations of Rk28. The spaces L1, L2 and Lp29. Fourier series: pointwise convergence30. Fourier series: convergence re-assessed31. L2-spaces: orthogonal sequences32. L2-spaces as Hilbert spaces33. Fourier transforms34. Integration in probability theoryAppendix IAppendix IIBibliographyNotation indexSubject index