Older versions of Qiuzhen Lectures on Analysis
Revision after this version: A major revision was made to Ch. 21 on Hilbert spaces. Sec. 27.5-27.7 on spectral theory was completely rewritten and moved to Ch. 25. I hope this new presentation of Riesz’s original treatment of the spectral theorem provides better insight into the monotone convergence extension, an important method in measure theory. The name of Ch. 27 was also changed to “completeness and duality in measure theory”.