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