2:15pm-3:55pm Monday and Wednesday in room 376 MSB.
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;
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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/RV2023.html |
Please, note the calendar below is just a plan. Homework dates WILL be adjusted during the semester!
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Date
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Lecture Topic
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Special Remarks
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Monday (08/21/23) |
Introduction (Why do we need measure theory?). Basic definition: ${\mathbb R}^d$. Basic topology. Compact sets. Heine-Borel theorem. | |
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Wednesday (08/23/23) |
Rectangles and cubes. More on Open/Closed set (fun with HW). | First Homework. |
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Monday (08/28/23) |
Rectangles and cubes. Cantor Set. | |
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Wednesdau (08/30/23) |
Cantor Set. Exterior Measure. | First Homework is due. Second Homework. |
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Monday (09/04/23) |
NO CLASS - Labor Day | |
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Wednesday (09/06/23) |
Exterior Measure. Lebesgue Measure. | |
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Monday (09/11/23) |
Lebesgue Measure. | |
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Wednesday (09/13/23) |
Lebesque Measure. | Second Homework is due. Third Homework. |
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Monday (09/18/23) |
Measurable Functions. | |
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Wednesday (09/20/23) |
Measurable Functions. | Third Homework is due Fourth Homework. |
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Monday (09/25/23) |
Measurable Functions. | |
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Wednesday (09/27/23) |
Measusrable Functions. | |
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Monday (10/02/23) |
Theorems of Egorov and Lusin/Integration. | |
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Wednesday (10/04/23) |
Theorems of Egorov and Lusin/Integration. | Fifth Homework. Fourth Homework is due. |
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Monday (10/09/23) |
More fun with integration! | |
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Wednesday (10/11/23) |
More fun With Integration (Bounded convergence) | Homework Six, Fifth HW is due |
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Monday (10/16/23) |
More fun with Integration! Integrability and Dominated Convergence | |
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Wednesday (10/18/23) |
L1 and dense sets in L1 | HW 6 is due. |
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MONDAY (10/23/23) |
Invariant Properties. Welcome to Fubini's Theorem | Home work 6 is due. Homework Seven. |
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Wednesday (10/25/23) |
Fubini's Theorem and applications | |
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Monday (10/30/23) |
Fubini Theorem and more | |
|
Wednesday (11/01/23) |
Maximal Function / Vitali covering | |
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Monday (11/06/23) |
Lebesgue differentiation theorem and applications. | Home work 7 is due. Homework Eight. |
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Wednesday (11/08/23) |
Lebesgue differentiation theorem and applications / Kernels. | |
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Monday (11/13/23) |
Welcome to Kernels. | |
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Wednesday (11/15/23) |
More on Kerlens. | Home work 8 is due. Homework Nine. |
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Monday (11/20/23) |
Functions of bounded variation. | |
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Wednesday (11/22/19) |
Thanksgiving recess - no classes | |
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Monday (11/27/23) |
Bounded variation and derivative (continuous case) | |
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Wednesday (11/29/23) |
Absolutely Continuous functions | HW nine is due. |
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Monday (12/4/23) |
LETS try to take derivative! | |
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Wednesday (12/6/23) |
Jumps | HW nine is due. FINAL HOME WORK |
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Sunday (12/17/23) |
FINAL HOME WORK IS DUE (EMAIL) | |