Textbook: "Real and Complex Analysis" 3rd Edition by Walter Rudin
Syllabus
L1: Measurable space, measurable function
L2: Borel set, simple function
L3 Integration of positive function
L4 Integration of complex function
L5 Set topology
L6 Riesz representation Theorem (I)
L7 Riesz representation Theorem (II), Borel measure
L8 Lebesgue measure, Lusin Theorem
L9 Lp spaces
L10 Complex measure
L11 Lebesgue-Radon-Nikodym Theorem
L12 Derivative of measure
L13 Differentiable transformation
L14 Product measure
L15 Fubini Theorem
L16 Convolution, distribution function
L17 Fourier transformation