Date | Topic | Reading | Assignments |
Aug 28 | Introduction, Riemann Integration | 1 | Homework 1
Solutions |
Aug 30 | Null Sets, Outer Measure | 2.1, 2.2 | |
Sept 4 | Lebesgue Measure, σ-fields | 2.3 | Homework 2
Solutions |
Sept 6 | Properties of Lebesgue Measure | 2.4 | Homework 1 due at 10:00am in Physics P-124. |
Sept 11 | Borel Measure. | 2.5. | Homework 3
Solutions |
Sept 13 | Probability Spaces, Measurable Functions |
2.6,2.7, 3.1,3.2,3.3 |
Homework 2 due at 10:00am in Physics P-124. |
Sept 18 | Properties of Measurable Functions | 3.4 | Homework 4
Solutions |
Sept 20 | Random Variables, Probability Distributions, Independence of Random Variables | 3.5 | Homework 3 due at 10:00am in Physics P-124. |
Sept 25 | Lebesgue Integral of non-negative measurable functions | 4.1 | Homework 5
Solutions |
Sept 27 | Monotone Convergence Theorems. | 4.2 | Homework 4 due at 10:00am in Physics P-124. |
Oct 2 | Integrable Functions. | 4.3 | Homework 6
Solutions |
Oct 4 | Dominated Convergence Theorem. | 4.4 | Homework 5 due at 10:00am in Physics P-124. |
Oct 9 | No Classes in Session | ||
Oct 11 | Relation to Riemann Integral | 4.5 | |
Oct 16 | Approximation of measurable functions | 4.6 | |
Oct 18 | Probability | 4.7 | Homework 6 due at 10:00am in Physics P-124. |
Oct 23 | L^{1} spaces. | 5.1 | |
Oct 25 | Midterm Exam 10-11:20am in Physics P-124
Exam (Solutions) |
Covers: 2.1-2.7, 3.1-3.5, 4.1-4.7 Except: 2.6.3, 3.5.5, 4.7.4, 4.7.5 |
Practice 1, (Solutions) Practice 2, (Solutions) |
Oct 30 | L^{2} spaces. | 5.2 | Homework 7
Solutions |
Nov 1 | L^{p} spaces. | 5.3 | |
Nov 6 | L^{p} spaces continued. | 5.3 | Homework 8
Solutions |
Nov 8 | Product Measures | Page 1-6 from here. | Homework 7 due at 10:00am in Physics P-124. |
Nov 13 | Fubini's Theorem | Page 6-9 from here. | Homework 9
Solutions |
Nov 15 | Product Measures Continued. | Page 9-12 from here. | Homework 8 due at 10:00am in Physics P-124. |
Nov 20 | Joint Distributions | 6.5.1,6.5.2 | |
Nov 22 | No Classes in Session | ||
Nov 27 | Joint Distributions continued. Radon-Nikodym Theorem. |
6.5.2,6.5.3 7.1 |
Homework 10
Solutions |
Nov 29 | Radon-Nikodym Theorem continued. | 7.1,7.2 | Homework 9 due at 10:00am in Physics P-124. |
Dec 4 | Radon-Nikodym Theorem continued and statement of the Lebesuge Decomposition Theorem. | 7.2 | |
Dec 6 | Review Session | Homework 10 due at 10:00am in Physics P-124. | |
Dec 20 | Final Exam 8:00am-10:45am in Physics P-124. | Exam Information | Practice 1, (Solutions) Practice 2 Practice 3 (Except Question 10). |