Real Analysis

Graduate course · Fall 2026 · 64 hours

Textbook: Real and Complex Analysis 3rd Edition by Walter Rudin

Syllabus

  1. L1: Measurable space, measurable function, Borel set
  2. L2: Simple function, integration of positive functions
  3. L3: Integration of complex functions
  4. L4: Set topology
  5. L5: Riesz representation Theorem
  6. L6: Properties of Borel measure, Lebesgue measure
  7. L7: Lusin Theorem, Lp spaces
  8. L8: Complex measure
  9. L9: Lebesgue-Radon-Nikodym Theorem
  10. L10: Riesz representation Theorem for complex measure
  11. L11: Derivative of measure
  12. L12: Differentiable transformation
  13. L13: Product measure
  14. L14: Fubini Theorem, completion of product measures, convolution
  15. L15: Distribution function, Fourier transformation
  16. L16: Translation-invariant subspace of L2, Schwarz space