Theory of Functions of a Real Variable I
Measurable spaces and functions. Measure spaces and integration. Extensions of set functions, outer measures, Lebesgue measure. Signed measures. Differentiation of set functions, Product measures, Lp-spaces.
Real Analysis Vol. 1: Modern Techniques and their Applications, Folland, 2nd edition, Wiley and Sons.
- Sets and Measures - Chapters 2, 3, 4
- Measurable Functions and the Lebesgue Integral - Chapters 5, 6, 7, 8, 10
- The Radon-Nikodym Theorem - Chapters 11, 12, 13
- Lp Spaces, duality - Chapter 15
- Hilbert spaces - Chapter 19
(Shao 2018 )