Textbook: "Real and Complex Analysis" 3rd Edition by Walter Rudin
Syllabus (68h)
L1: Measurable space, measurable function, Borel set
L2: Simple function, integration of positive functions
L3 Integration of complex functions
L4 Set topology
L5 Riesz representation Theorem
L6 Properties of Borel measure, Lebesgue measure
L7 Lusin Theorem, Lp spaces
L8 Complex measure
L9 Lebesgue-Radon-Nikodym Theorem
L10 Riesz representation Theorem for complex measure
L11 Derivative of measure
L12 Differentiable transformation
L13 Product measure
L14 Fubini Theorem, completion of product measures, convolution
L15 Distribution function, Fourier transformation
L16 Translation-invariant subspace of L2, Schwarz space
L17 Fourier Analysis in tempered distribution spaces