01:10pm-2:00pm Monday, Tuesday, Wednesday and Thursday in room 211 MSB.
Also note:
Section Start Date 08/29/16; Section End Date 12/11/16; Last Day to Add 09/04/16; Last Day to Drop 09/11/16; Last Day to Withdraw 11/06/16;
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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. 10:30-12:00 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/RV2016.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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Monday (08/29/16) |
Introduction (Why do we need measure theory?). Basic definition: ${\mathbb R}^d$ and a bit of topology. | |
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Tuesday (08/30/16) |
More of topology. Compact sets. | |
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Wednesday (08/31/16) |
Heine-Borel theorem. Rectangles and cubes. | First Homework. |
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Thursday (09/01/16) |
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Monday (09/05/16) |
Labor Day - no classes. | |
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Tuesday (09/06/16) |
Open/Closed set (fun with HW). Cantor Set. | |
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Wednesday (09/07/16) |
Cantor Set | First Homework is due. Second Homework. |
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Thursday (09/08/16) |
Examples and Counting with cubes. | |
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Monday (09/12/16) |
Exterior Measure | |
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Tuesday (09/13/16) |
Exterior Measure. | |
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Wednesday (09/14/16) |
Lebesque Measure | Second Homework is due. Third Homework. |
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Thursday (09/15/16) |
Measuarable Sets | |
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Monday (09/19/16) |
Lebesque Measure | |
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Tuesday (09/20/16) |
Lebesque Measure | |
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Wednesday (09/21/16) |
Non measurable set | Forth Homework. |
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Thursday (09/22/16) |
Boreel Sigma-Algebra, Measurable Functions. | |
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Monday (09/26/16) |
Measurable Functions. | Third Homework is due. |
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Tuesday (09/27/16) |
Measurable Functions | |
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Wednesday (09/28/16) |
Egorov's Theorem | Fourth Homework is due. Fifth Homework. |
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Thursday (09/29/16) |
Lusin theorem. Welcome to integration. | |
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Monday (10/03/16) |
Integration. | |
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Tuesday (10/04/16) |
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Wednesday (10/05/16) |
Fifth Homework is due. Sixt Homework. | |
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Thursday (10/06/16) |
Monotone Convergence theorem. | |
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Monday (10/10/16) |
Dominated Convergense Theorem. | |
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Tuesday (10/11/16) |
$L_1$ space. Completeness of $L_1$. | |
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Wednesday (10/12/16) |
Examples of families which are dense in $L_1$. | Sixt Homework is due. Seventh Homework. |
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Thursday (10/13/16) |
Invariance Properties. Fubini's Theorem. | |
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Monday (10/17/16) |
Fubini's Theorem. | |
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Tuesday (10/18/16) |
Fubini's Theorem | |
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Wednesday (10/19/16) |
Fubini's Theorem: appliacations. | |
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Thursday (10/20/16) |
Fubini's Theorem: appliacations. | |
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Monday (10/24/16) |
Differentiation and Integration: Hardy-Littlewood maximal function. | Seventh Homework is due. Homework Eight. |
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Tuesday (10/25/16) |
Differentiation and Integration: Hardy-Littlewood maximal function. | |
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Wednesday (10/26/16) |
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Thursday (10/27/16) |
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Monday (10/31/16) |
Kernels | |
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Tuesday (11/01/16) |
Kernels | |
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Wednesday (11/02/16) |
Functions of Bounded Variation. | |
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Thursday (11/03/16) |
F. Riesz Lemma and rising sun | |
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Monday (11/07/16) |
Differentiability and bounded variation. | Eights Homework is due. Ninth Homework. |
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Tuesday (11/08/16) |
Differentiability and bounded variation | |
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Wednesday (11/09/16) |
The Cabtor-Lebesgue function and "Fundamental Theorem of calculus". | |
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Thursday (11/10/16) |
Absolutely continuous functions | |
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Monday (11/14/16) |
Vitali covering and differentiability of absolutely continuous functions. | |
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Tuesday (11/15/16) |
Differentiability of jump functions | |
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Wednesday (11/16/16) |
Differentiability of jump functions | |
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Thursday (11/17/16) |
Length of a rectifiable curve. | |
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Monday (11/21/16) |
Welcome to $L_2(\mathbb{R}^d)$ | Ninth Homework is due. Tens Homework. |
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Tuesday (11/22/16) |
Hilbert Spaces | |
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Wednesday (11/23/16) |
Thanksgiving recess - no classes | |
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Thursday (11/24/16) |
Thanksgiving recess - no classes | |
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Monday (11/28/16) |
Hilber spaces | |
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Tuesday (11/29/16) |
Hilbert space and the basis. | |
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Wednesday (11/30/16) |
Fourier Series | Tens Homework is due. |
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Thursday (12/01/16) |
Fourier Series. Closed Subspaces. | Ellevens Homework. |
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Monday (11/05/16) |
Closed Subspaces and orthogonal projections. | FINAL HOMEWORK |
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Tuesday (11/06/16) |
Closed Subspaces and orthogonal projections. | |
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Wednesday (11/07/16) |
Linear Transformations | |
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Thursday (12/08/16) |
Linear Transformations | |
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10:15 - 12:30 p.m. Tues. Dec. 13 |
FINAL EXAM (FINAL HOME WORK DUE) | |