- We will pretty mych cover chapters 0-3 of:
Gerald B. Folland, Real analysis: modern techniques and their applications, 2nd ed.
- Measures, outer measures
- Borel measures on the real line, non-measurable sets
- Measurable Functions
- Littlewood's three principles
- Integration of Nonnegative Functions
- Integration of Complex Functions
- Modes of Convergence
- Product Measures
- The n-dimensional Lebesgue Integral
- Integration in Polar Coordinates
3 Signed Measures and Differentiation
- The Hardy-Littlewood maximal function
- Signed Measures
- The Lebesgue-Radon-Nikodym Theorem
- Complex Measures
- Differentiation on Euclidean Space
- Functions of Bounded Variation
- Useful reading, for Real Analysis I and Real Analysis II:
Folland, G.B. (1984). Real Analysis, New York, Wiley.
Roydan, H.L. (1969). Real Analysis, New York, MacMillan
Rudin, W. (1986). Real and Complex Analysis, New York, McGraw Hill (3rd edition).
Stein, E.M. and Sharkarchi, R. (2005). Real Analysis, Measure Theory, Integration and Hilbert Spaces, Princeton University Press.
Wheeden, R. and Zygmund, A. (1977). Measure and Integral, An Introduction to Real Analysis, New York, M. Dekker.
Rudin, W. (1976). Principles of Mathematical Analysis, New York. McGraw Hill. (3rd edition).
Stein, E.M. and Sharkarchi, R. (2003). Fourier Analysis, Princeton University Press.
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