### 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 **R**^{d}. *L ^{p}* spaces: Cauchy-Bunyakovsky-Schwarz, Hoelder, Minkowski and Jensen inequalities,

*L*

^{2}and

*L*spaces as Hilbert and Banach spaces, Riesz representation theorem for bounded functionals on

^{p}*L*. Integration on product spaces, Fubini's and Tonelli's theorems, Fourier transform and Plancherel theorem. For prelim preparation, see the prelim study guide.

^{p}**Prerequisites:** MATH 5110.

**Offered:** Spring

**Credits:** 3

**Sections: **Spring 2011 on Storrs Campus

PSCourseID | Course | Sec | Comp | Time | Room | Instructor |
---|---|---|---|---|---|---|

02700 | 5111 | 001 | Lecture | TuTh 12:30:00 PM-1:45:00 PM | MSB215 | Evarist Gine-Masdeu |