Math 5111 : Real Analysis (Measure and Integration)
Spring 2012
Alexander Teplyaev

course time and room: TuTh 9:30-10:45am, MSB 415

The course is open for all graduate students who passed 5110, and to other students by permission; the course can be repeated either as an audit or as an independent study (don't hesitate to ask for permission if needed).

office: MSB M222 -- office hours: check this link
phone: (860)486-3206


See also   Math 6010 : Seminar in Analysis



Real Analysis for Graduate Students: Measure and Integration Theory by Richard Bass (special note: you are not allowed to print books on departmental printers)

Course description

5111 --- Abstract integration: Lebesgue integration theory, outer measures and Caratheodory's theorem, Fatou's lemma, monotone and dominated convergence theorems. Measure theory: positive Borel measures, Riesz representation theorem for positive linear functionals on C(K), complex measures, Hahn-Jordan and Lebesgue decompositions, Radon-Nykodim theorem and differentiation of measures, Riemann-Stieltjes integral, the Lebesgue measure on Rd. Lp spaces: Cauchy-Bunyakovsky-Schwarz, Hoelder, Minkowski and Jensen inequalities, L2 and Lp spaces as Hilbert and Banach spaces, Riesz representation theorem for bounded functionals on Lp. Integration on product spaces, Fubini's and Tonelli's theorems, Fourier transform and Plancherel theorem. See also Real Analysis Prelim Study Guide. Textbook choices: Real Analysis for Graduate Students: Measure and Integration Theory by Rich Bass. Real and Complex Analysis by W. Rudin. Real Analysis and Probability by R.M. Dudley. Real Analysis: Modern Techniques and Their Applications by G. Folland. Supplementary reading: Real Analysis by H. Royden and P. Fitzpatrick. Real Analysis: Measure Theory, Integration, and Hilbert Spaces by E.M. Stein and R. Shakarchi. Measure and Integral by R.L. Wheeden and A. Zygmund.