# Spring 2015 MATH 202B 001 LEC

Section | Days/Time | Location | Instructor | CCN |
---|---|---|---|---|

001 LEC | MWF 9-10A | 241 CORY | RIEFFEL, M A | 54383 |

Units/Credit | Final Exam Group | Enrollment |
---|---|---|

4 | 4: MONDAY, MAY 11, 2015 7-10P | Limit:36 Enrolled:30 Waitlist:0 Avail Seats:6 [on 03/22/15] |

**Prerequisites:** 202A and 110.

**Syllabus:** Measure and integration. Product measures and Fubini-type theorems. Signed measures; Hahn and Jordan decompositions. Radon-Nikodym theorem. Integration on the line and in Rn. Differentiation of the integral. Hausdorff measures. Fourier transform. Introduction to linear topological spaces, Banach spaces and Hilbert spaces. Banach-Steinhaus theorem; closed graph theorem. Hahn-Banach theorem. Duality; the dual of LP. Measures on locally compact spaces; the dual of C(X).

**Office:** 811 Evans

**Office Hours:** TBA

**Required Text:** none

**Recommended Reading:** "Real and Functional Analysis" 3rd ed. by Serge Lang, Springer-Verlag.

"Basic Real Analysis" by Anthony Knapp. "Advanced Real Analysis" by Anthony Knapp. My understanding is that through an agreement between UC and Springer, chapters of the Knapp texts are availablefor free download by students. See the course webpage

**Grading:** There will be a final examination on Monday May 11, 7-10 PM , which will count for35% of the course grade. There will be a midterm exam at the regular class time. It will count for 15% of the course grade. There will be no early or make-up final examination. Nor will a make-up midterm exam be given; instead, if you tell me ahead of time that you must miss the midterm exam, then the final exam will count for 50% of your course grade. If you miss the midterm exam but do not tell me ahead of time, then you will need to bring me a doctor's note or equivalent in order to have the final exam count for 50% of your course grade.

**Course content: **We will use the measure theory begun in Math 202A to develop thetheory of integration, from the beginning.My treatment of integration will be closer to that given in the text byLang than in the text by Knapp. Thus we will basically be doing Bochner-Lebesgue integration, but I will not assume any prioracquaintance with Banach spaces.Topics that will be discussed after the basic theory is developedinclude product measures and Fubini theorems, signed measures, theRadon-Nikodym theorem, and measure and integration on locally compactspaces. We will also go through an introduction to functional analysis.Banach spaces, closed-graph theorem, Hahn-Banach theorem andduality, duals of classical Banach spaces, weak topologies, Alaoglu theorem, convexity and Krein-Milman theorem.<br>In my lectures I willtry to give well-motivated careful presentations of the material.

**Comment: **Students who need special accomodation for examinations should bring me the appropriate paperwork, and must tell me at least a week in advance what specific accomodation they need, so that I will have enough time to arrange it.

**Course Webpage:** math.berkeley.edu/~rieffel/