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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.

Credit Hours: 


  1. Sets and Measures - Chapters 2, 3, 4
  2. Measurable Functions and the Lebesgue Integral - Chapters 5, 6, 7, 8, 10
  3. The Radon-Nikodym Theorem - Chapters 11, 12, 13
  4. Lp Spaces, duality - Chapter 15
  5. Hilbert spaces - Chapter 19

(Shao 2018 )

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