Functions of Real Variables 1 (62051/72051)

2:15pm-4:15pm (note special time instead of 3:55) Tuesdayvand Thursday in room 211 MSB.

Syllabus.

Also note:

Section Start Date 08/22/19; Section End Date 12/08/19; Last Day to Add 08/28/19; Last Day to Drop 09/04/19; Last Day to Withdraw 10/30/19;

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.
"An Introduction to Measure Theory" by Terrence Tao.
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/RV2019.html

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

Date
Lecture Topic
Special Remarks
Thursday (08/22/19)
Introduction (Why do we need measure theory?). Basic definition: ${\mathbb R}^d$. Basic topology. Compact sets. Heine-Borel theorem.
Tuesday (08/27/19)
Rectangles and cubes. More on Open/Closed set (fun with HW). Cantor Set. First Homework.
Thursday (08/29/19)
Exterior Measure.
Tuesday (09/03/19)
Exterior Measure/ Lebesque Measure and Measurable Sets. First Homework is due. Second Homework.
Thursday (09/05/19)
(No CLASS NEED TO MAKE UP/add 20 min to each class)
Tuesday (09/10/19)
Lebesque Measure and Measurable Sets.
Thursday (09/12/19)
Measurable and Non- Measurable Sets. Second Homework is due. Third Homework.
Tuesday (09/17/19)
Welcome to Measurable Functions.
Thursday (09/19/19)
Measurable Functions. Third Homework is due
Tuesday (09/24/19)
Theorems of Egorov and Lusin. Fourth Homework.
Thursday (09/26/19)
Integration (Bounded Convergence, Lebesgue vs Riemann).
Tuesday (10/01/119)
Integration (Monotone convergence). Fifth Homework. Fourth Homework is due.
Thursday (10/03/19)
Integration and Welcome to $L_1$
Tuesday (10/8/19)
Riesz-Fischer Theorem, Invariance Properties. Fubini's Theorem
Thursday (10/10/19)
Fall break (NO CLASS)
Tuesday (10/15/19)
More on Fubini's Theorem Fifth HW is due
Thursday (10/17/19)
More on Fubini's Theorem Homework Six.
Tuesday (10/22/19)
The Hardy-Littlewood maximal function.
Thursday (10/24/19)
The Lebesque differentiation theorem.
Tuesday (10/29/19)
Welcome to Kernels. Home work 6 is due. Homework Seven.
Thursday (11/31/19)
More on Kerlens.
Tuesday (11/05/19)
Functions of bounded variation. Home work 7 is due. Homework Eight.
Thursday (11/07/19)
Tuesday (11/12/19)
Bounded variation and derivative (continuous case) Homework Eight is due
Thursday (11/14/19)
Absolutely Continuous functions
Tuesday (11/19/19)
Jumps and removal of continuity assumption. Homework Nine.
Thursday (11/21/19)
Mikowski and the length of the curve.
Tuesday (11/26/19)
Minkowski and the length of the curve Homework Ten. Homework Nine is due.
Thursday (11/28/19)
Thanksgiving recess - no classes Final Homework.
Tuesday (12/03/19)
Welcome to Hilbert Space.
Thursday (12/05/19)
Welcome to Hilbert Space Homework ten is due
December 13, 10 a.m.
FINAL HOME WORK DUE

TO ARTEM ZVAVITCH'S HOMEPAGE