| Week |
Day |
Date |
Main Topic |
Examination Dates |
| 01 |
M |
AUG/24 |
Motivating
examples for Measure Theory |
|
| W |
AUG/26 |
Sigma-fields |
|
|
| F |
AUG/28 |
Measures | ||
| 02 |
M |
AUG/31 |
Borel
sigma-field |
|
| W |
SEP/02 |
C.D.F.'s |
||
| F |
SEP/04 |
Sigma-finiteness |
||
| 03 |
M |
SEP/07 |
Labor
Day |
|
| W |
SEP/09 |
Pi-Lambda
Theorem |
Answerkey Quiz #1 |
|
| F |
SEP/11 |
Caratheodary's
Extension Theorem |
||
| 04 |
M |
SEP/14 |
The
Lebesgue Measure |
|
| W |
SEP/16 |
Borel-Cantelli
Lemmas |
||
| F |
SEP/18 |
More
on the Borel-Cantelli
Lemmas |
||
| 05 |
M |
SEP/21 |
Independence |
|
| T |
SEP/22 |
N/A |
Answerkey Exam
#1 (5-6:30pm) AUG/24-SEP/18 @ ECCR 131 |
|
| W |
SEP/23 |
More
on Independence |
||
| F |
SEP/25 |
Tail Events | ||
| 06 |
M |
SEP/28 |
Measurable Functions | |
| W |
SEP/30 | More on Measurable Functions | ||
| F |
OCT/02 |
Forward
Measures |
||
| 07 |
M |
OCT/05 |
The
Extended Borel sigma-field |
|
| W |
OCT/07 |
Integration
of Simple Functions |
||
| F |
OCT/09 |
Approximation
by Simple Functions |
||
| 08 |
M |
OCT/12 |
Integration
of Measurable Functions |
|
| W |
OCT/14 |
More
on Integration |
||
| F |
OCT/16 |
Useful
Inequalities |
||
| 09 |
M |
OCT/19 |
More
Inequalities |
|
| W |
OCT/21 |
Large
Deviations |
Answerkey Quiz #2 | |
| F |
OCT/23 |
More
on Large
Deviations |
||
| 10 |
M |
OCT/26 |
Sigma-fields
associated with Random Variables |
|
| T |
OCT/27 |
N/A |
Answerkry Exam
#2 (5-6:30pm) SEP/21-OCT/21 @ ECCR 131 |
|
| W |
OCT/28 |
More on Sigma-fields and Random Variables | ||
| F |
OCT/30 |
Convergence
in Lp-norm |
||
| 11 |
M |
NOV/02 |
Convergence
in Probability |
|
| W |
NOV/04 |
More
on Convergence of Random Variables |
||
| F |
NOV/06 |
Absolute
Continuity of Measures |
||
| 12 |
M |
NOV/09 |
Radon-Nikodyn
Derivatives |
|
| W |
NOV/11 |
Conditional
Expectation and Probability |
||
| F |
NOV/13 |
Properties
of the Conditional Expectation |
||
| 13 |
M |
NOV/16 |
More
on Conditional Expectation |
|
| W |
NOV/18 |
The Orthogonal Projection Theorem in L2 | ||
| F |
NOV/20 |
The Lebuesgue Decomposition Theorem | ||
| 14 |
M |
NOV/23 |
Fall Break | |
| W |
NOV/25 |
Fall Break | ||
| F |
NOV/27 |
Fall Break | ||
| 15 |
M |
NOV/30 |
Product
Spaces |
|
| W |
DEC/02 |
Existence
and Uniqueness of Product Measures |
||
| F |
DEC/04 |
Measurability
in Product Spaces |
Answerkey Quiz #3 | |
| S |
DEC/05 |
Makeup
Lectures 3:15-4:45pm @ ECCR 110 |
||
| 16 |
M |
DEC/07 |
Fubini's
Theorem |
|
| T |
DEC/08 |
N/A |
Answerkey Exam
#3 (5-6:30pm) OCT/26-DEC/04 @ ECCR 131 |
|
| W |
DEC/09 |
Applications
of Product Spaces |
||
| F |
DEC/11 |
Countable
product of measurable spaces |