Preliminaries.- 1. Metric and Normed Spaces.- 2. Lebesgue Measure.- 3. Measurable Functions.- 4. The Lebesgue Integral.- 5. Differentiation.- 6. Absolute Continuity and the Fundamental Theorem of Calculus.- 7. The L p Spaces.- 8. Hilbert Spaces and L^2( E ).- 9. Convolution and the Fourier Transform.
Have been slowly working through Heil's book. It's a decent book for the neophyte in measure theory. The discussions are good. The presentation and organization of the material is also good. The problems are hard for me to be honest as Heil does'nt simply apply the theory developed in the chapter to the problems but uses them to extend it.