Measure, Integration & Real Analysis (Axler)

Sheldon Axler, Measure, Integration & Real Analysis, Springer GTM 282, 2020. Open access — the free electronic edition lives at measure.axler.net.

Covers Riemann integration and its limitations, measures and their construction, integration, differentiation, product measures, Banach and Hilbert spaces, \(L^p\) spaces, real and complex measures, spectral theory for compact operators, and probability measures. Exercises sit at the end of each section (1A, 1B, …), with no printed answers.

Solutions to every exercise live at Solutions to Axler’s Measure, Integration & Real Analysis.