Functions of Real Variables 1 (62051/72051)

2:15pm-3:55pm Monday and Wednesday in room 376 MSB.

Syllabus.

Also note:

Section Start Date 08/21/23; Section End Date 12/10/23; Last Day to Add 08/27/23; Last Day to Drop 09/03/23; Last Day to Withdraw 10/29/23;

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/RV2023.html

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

Date
Lecture Topic
Special Remarks
Monday (08/21/23)
Introduction (Why do we need measure theory?). Basic definition: ${\mathbb R}^d$. Basic topology. Compact sets. Heine-Borel theorem.
Wednesday (08/23/23)
Rectangles and cubes. More on Open/Closed set (fun with HW). First Homework.
Monday (08/28/23)
Rectangles and cubes. Cantor Set.
Wednesdau (08/30/23)
Cantor Set. Exterior Measure. First Homework is due. Second Homework.
Monday (09/04/23)
NO CLASS - Labor Day
Wednesday (09/06/23)
Exterior Measure. Lebesgue Measure.
Monday (09/11/23)
Lebesgue Measure.
Wednesday (09/13/23)
Lebesque Measure. Second Homework is due. Third Homework.
Monday (09/18/23)
Measurable Functions.
Wednesday (09/20/23)
Measurable Functions. Third Homework is due Fourth Homework.
Monday (09/25/23)
Measurable Functions.
Wednesday (09/27/23)
Measusrable Functions.
Monday (10/02/23)
Theorems of Egorov and Lusin/Integration.
Wednesday (10/04/23)
Theorems of Egorov and Lusin/Integration. Fifth Homework. Fourth Homework is due.
Monday (10/09/23)
More fun with integration!
Wednesday (10/11/23)
More fun With Integration (Bounded convergence) Homework Six, Fifth HW is due
Monday (10/16/23)
More fun with Integration! Integrability and Dominated Convergence
Wednesday (10/18/23)
L1 and dense sets in L1 HW 6 is due.
MONDAY (10/23/23)
Invariant Properties. Welcome to Fubini's Theorem Home work 6 is due. Homework Seven.
Wednesday (10/25/23)
Fubini's Theorem and applications
Monday (10/30/23)
Fubini Theorem and more
Wednesday (11/01/23)
Maximal Function / Vitali covering
Monday (11/06/23)
Lebesgue differentiation theorem and applications. Home work 7 is due. Homework Eight.
Wednesday (11/08/23)
Lebesgue differentiation theorem and applications / Kernels.
Monday (11/13/23)
Welcome to Kernels.
Wednesday (11/15/23)
More on Kerlens. Home work 8 is due. Homework Nine.
Monday (11/20/23)
Functions of bounded variation.
Wednesday (11/22/19)
Thanksgiving recess - no classes
Monday (11/27/23)
Bounded variation and derivative (continuous case)
Wednesday (11/29/23)
Absolutely Continuous functions HW nine is due.
Monday (12/4/23)
LETS try to take derivative!
Wednesday (12/6/23)
Jumps HW nine is due. FINAL HOME WORK
Sunday (12/17/23)
FINAL HOME WORK IS DUE (EMAIL)

TO ARTEM ZVAVITCH'S HOMEPAGE