Course Description  Basics of normed vector spaces and Hilbert spaces, bounded linear operators and functionals, L^{p} spaces, fundamental theorems for Banach spaces and bounded lienar functionals, weak convergence. topological spaces, locally compact Hausdorff spaces, compactness theorems, topological vector spaces, Radon measures, regularity and approximations, Riesz representation theorem, the dual of C_{c}(X) and the dual of C_{0}(X). 
Prerequisites  Math 140 ABC and Math 240A, or equivalent. 
Textbook  Gerald B. Folland, Real Analysis: Modern Techniques and Applications, 2nd edition, Wiley, 1999. We will cover part of Chapters 4  7. 
Topics of lectures 

Lectures  10:00 am  10:50 am, Mondays, Wednesdays, and Fridays, AP&M 5402. 
Instructor  Professor Bo Li. Office: AP&M 5723. Phone: (858) 5346932. Email: bli@math.ucsd.edu. Office hours: 11:00 am  12:00 noon, Mondays, and 1:00 pm  1:30 pm, Wednesdays. 
Grader  Yunyi Zhang. Office: 1256. Email: yuz334@ucsd.edu. 
Homework 
Homework is assigned, collected, and partially graded regularly.
Each homework assingment is due at the beginning of class of the due date.
Note: Please print your names and student ID nubmers on your homework. Please stable together your homework pages. Note: no late homework will be accepted unless a written verification of a valid excuse (such as hospitalization, family emergency, religious observance, court appearance, etc.) is provided.

Exams 
There will be one midterm and one final, closebook and closenote exams.
The final exam will be cumulative.
Midterm exam: 10:00 am  10:50 am, Friday, February 13, 2020, AP&M 5402. Final exam: 8:00 am  10:59 am, Friday, March 20, 2020. Place: To be announced. Note: neither rescheduled nor makeup exams will be allowed unless a written verification of a valid excuse (such as hospitalization, family emergency, religious observance, court appearance, etc.) is provided. 
Grading  The final course grade will be determined based on the homework and exams with the weights: homework  30%, midterm exam  30%, and final exam  40%. 