Functions of Real Variables 1 (62051/72051)

2:15pm-3:55pm Monday and Wednesday in room 276 MSB.

Syllabus.

Also note:

Section Start Date 08/19/24; Section End Date 12/08/24; Last Day to Add 08/25/24; Last Day to Drop 09/01/24; Last Day to Withdraw 10/27/24;

Instructor:
Book:
Book:
Office hours:
Office:
Office tel.:
E-mail:
WWW of the course :
Artem Zvavitch
"Real Analysis: Measure Theory, Integration, and Hilbert Spaces" by E. M. Stein, R. Shakarchi.

12:30-2:00 TR, but the best is to e-mail me and to make an appointment.
364
(330)-672-33-16
zvavitch@math.kent.edu
http://www.math.kent.edu/~zvavitch/RVFall2024.html

Please, note the calendar below is just a plan. Homework dates WILL be adjusted during the semester!

Date
Lecture Topic
Special Remarks
Monday (08/19/24)
Introduction (Why do we need measure theory?). Basic definition: ${\mathbb R}^d$. Basic topology. Compact sets. Heine-Borel theorem.
Wednesday (08/21/24)
Rectangles and cubes. More on Open/Closed set (fun with HW). First Homework.
Monday (08/26/24)
Rectangles and cubes.
Wednesdau (08/28/24)
Cantor Set. Exterior Measure. First Homework is due. Second Homework.
Monday (09/02/24)
NO CLASS - Labor Day
Wednesday (09/04/24)
Exterior Measure. Lebesgue Measure.
Monday (09/09/24)
Exterior Measure and Lebesgue Measure.
Wednesday (09/11/24)
Lebesque Measure. Second Homework is due. Third Homework.
Monday (09/16/24)
Lebesgue Measure
Wednesday (09/18/24)
Measurable Functions.
Monday (09/23/24)
Measurable Functions.
Wednesday (09/25/24)
Theorems of Egorov and Lusin/Integration. Third Homework is due Fourth Homework.
Monday (09/30/24)
Integration.
Wednesday (10/02/24)
Integration.
Monday (10/07/24)
More fun with integration! (Bounded convergence)
Wednesday (10/09/24)
More fun With Integration Fifth Homework. Fourth Homework is due.
Monday (10/14/24)
More fun with Integration! Integrability and Dominated Convergence
Wednesday (10/16/24)
L1 and dense sets in L1 HW 6 is due.
MONDAY (10/21/24)
Invariant Properties. Welcome to Fubini's Theorem Home work 5 is due. Homework Six.
Wednesday (10/23/24)
Fubini's Theorem and applications
Monday (10/28/24)
Fubini Theorem and more
Wednesday (10/30/24)
Maximal Function / Vitali covering
Monday (11/04/24)
Lebesgue differentiation theorem and applications. Home work 7 is due. Homework Eight.
Wednesday (11/06/24)
Lebesgue differentiation theorem and applications / Kernels.
Monday (11/11/24)
Veterans Day No CLASS
Wednesday (11/13/24)
Kerlens. Home work 8 is due. Homework Nine.
Monday (11/18/24)
Functions of bounded variation.
Wednesday (11/20/24)
TBA
Monday (11/26/24)
Bounded variation and derivative (continuous case)
Wednesday (11/27/24)
THANKSGIVING BREAK, NO CLASS
Monday (12/2/24)
LETS try to take derivative!
Wednesday (12/4/24)
Jumps HW nine is due. FINAL HOME WORK
Sunday (12/15/24)
FINAL HOME WORK IS DUE (EMAIL)

TO ARTEM ZVAVITCH'S HOMEPAGE