College of Liberal Arts and Sciences

# Department of Mathematics

## Course Info

### MATH 5111: Real Analysis

Description: 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. For prelim preparation, see the prelim study guide.

Prerequisites: MATH 5110.

Offered: Spring

Credits: 3

### MATH 5111 - Section 1: Measure Theory

Description: 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.

Credits: 3

Sections: Spring 2016 on Storrs Campus

PSCourseID Course Sec Comp Time Room Instructor
02501 5111 001 Lecture TuTh 02:00:00 PM-03:15:00 PM MSB203 Chousionis, Vasilis