INSTRUCTOR: Professor Karin Reinhold,  ES 128C,  phone 442-4641
Office hours:   open door policy    -   or by appt.,  or by e-mail.
TEXT: Real Analysis, (third edition),
by H. L. Royden, editor: Prentice Hall.
Prerequisits: math 511 or permission of instructor.
Math 510A centers in the study of the Lebesgue measure and the Lebesgue integral. We will study the basic properties of the Lebesgue integral, measurable functions, Egorov's Theorem, Lusin's Theorem, integrable functions, convergence theorems (Fatou's, monotone convergence Thm., dominated convergence thm.), $L^p$ spaces and inequalities, differentiation of the integral, integration in product spaces (Fubbini's Theorem) and the Radon-Nicodym derivative. Ths course gives you the basic preparation for the Real Analysis Preliminary Exam.

Your grade in the course will be based on 4 in class exams, A temptative schedulle for the exams is as follows:

Exam 1:Feb. 12 Chapters 1, 2, 3.
Feb. 19 - 23no classes, winter break
Exam 2: Mar. 12Sections: 3.5,3.6,4.1, 4.2 if covered by Friday Mar 9.
Apr. 2 - Apr 9no classes, Spring Break
Exam 3: Apr. 16 4.2, 4.3. 4.4, 4.5., Chapter 6.
Exam 4: May 7 Product spaces. Fubini's Theorem. Radon-Nikodym theorem if time allows.