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, Lebesgue-Radon-Nikodym Theorem
L9 Riesz representation Theorem for complex measure
L10 Derivative of measure
L11 Differentiable transformation
L12 Product measure, Fubini Theorem
L13 Convolution, distribution function
L14 Fourier transformation
L15 Fourier transformation in L2
L16-17 Fourier Analysis in Euclidean spaces (complementary topic, if time is not limited)