2:15pm-3:55pm Monday and Wednesday in room 276 MSB.
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;
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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!
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Date
|
Lecture Topic
|
Special Remarks
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|
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. |
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Monday (08/26/24) |
Rectangles and cubes. | |
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Wednesdau (08/28/24) |
Cantor Set. Exterior Measure. | First Homework is due. Second Homework. |
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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. | |
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Wednesday (09/11/24) |
Lebesque Measure. | Second Homework is due. Third Homework. |
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Monday (09/16/24) |
Lebesgue Measure | |
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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. | |
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Wednesday (10/02/24) |
Integration. | |
|
Monday (10/07/24) |
More fun with integration! (Bounded convergence) | |
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Wednesday (10/09/24) |
More fun With Integration | Fifth Homework. Fourth Homework is due. |
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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. |
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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. |
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Wednesday (11/06/24) |
Lebesgue differentiation theorem and applications / Kernels. | |
|
Monday (11/11/24) |
Veterans Day No CLASS | |
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Wednesday (11/13/24) |
Kerlens. | Home work 8 is due. Homework Nine. |
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Monday (11/18/24) |
Functions of bounded variation. | |
|
Wednesday (11/20/24) |
TBA | |
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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 |
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Sunday (12/15/24) |
FINAL HOME WORK IS DUE (EMAIL) | |