2:15pm-4:15pm (note special time instead of 3:55) Tuesdayvand Thursday in room 211 MSB.
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;
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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. "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!
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Date
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Lecture Topic
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Special Remarks
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Thursday (08/22/19) |
Introduction (Why do we need measure theory?). Basic definition: ${\mathbb R}^d$. Basic topology. Compact sets. Heine-Borel theorem. | |
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Tuesday (08/27/19) |
Rectangles and cubes. More on Open/Closed set (fun with HW). Cantor Set. | First Homework. |
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Thursday (08/29/19) |
Exterior Measure. | |
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Tuesday (09/03/19) |
Exterior Measure/ Lebesque Measure and Measurable Sets. | First Homework is due. Second Homework. |
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Thursday (09/05/19) |
(No CLASS NEED TO MAKE UP/add 20 min to each class) | |
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Tuesday (09/10/19) |
Lebesque Measure and Measurable Sets. | |
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Thursday (09/12/19) |
Measurable and Non- Measurable Sets. | Second Homework is due. Third Homework. |
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Tuesday (09/17/19) |
Welcome to Measurable Functions. | |
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Thursday (09/19/19) |
Measurable Functions. | Third Homework is due |
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Tuesday (09/24/19) |
Theorems of Egorov and Lusin. | Fourth Homework. |
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Thursday (09/26/19) |
Integration (Bounded Convergence, Lebesgue vs Riemann). | |
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Tuesday (10/01/119) |
Integration (Monotone convergence). | Fifth Homework. Fourth Homework is due. |
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Thursday (10/03/19) |
Integration and Welcome to $L_1$ | |
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Tuesday (10/8/19) |
Riesz-Fischer Theorem, Invariance Properties. Fubini's Theorem | |
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Thursday (10/10/19) |
Fall break (NO CLASS) | |
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Tuesday (10/15/19) |
More on Fubini's Theorem | Fifth HW is due |
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Thursday (10/17/19) |
More on Fubini's Theorem | Homework Six. |
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Tuesday (10/22/19) |
The Hardy-Littlewood maximal function. | |
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Thursday (10/24/19) |
The Lebesque differentiation theorem. | |
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Tuesday (10/29/19) |
Welcome to Kernels. | Home work 6 is due. Homework Seven. |
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Thursday (11/31/19) |
More on Kerlens. | |
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Tuesday (11/05/19) |
Functions of bounded variation. | Home work 7 is due. Homework Eight. |
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Thursday (11/07/19) |
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Tuesday (11/12/19) |
Bounded variation and derivative (continuous case) | Homework Eight is due |
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Thursday (11/14/19) |
Absolutely Continuous functions | |
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Tuesday (11/19/19) |
Jumps and removal of continuity assumption. | Homework Nine. |
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Thursday (11/21/19) |
Mikowski and the length of the curve. | |
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Tuesday (11/26/19) |
Minkowski and the length of the curve | Homework Ten. Homework Nine is due. |
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Thursday (11/28/19) |
Thanksgiving recess - no classes | Final Homework. |
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Tuesday (12/03/19) |
Welcome to Hilbert Space. | |
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Thursday (12/05/19) |
Welcome to Hilbert Space | Homework ten is due |
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December 13, 10 a.m. |
FINAL HOME WORK DUE | |