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## MAT 324: Real Analysis

General information about the course

 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 L1 spaces. 5.1 Oct 25 Midterm Exam 10-11:20am in Physics P-124 Exam (Solutions) Covers: 1,2.1-2.7,3.1-3.5,4.1-4.7 Except: 2.6.3, 3.5.5, 4.7.4, 4.7.5 Practice 2, (Solutions) Oct 30 L2 spaces. 5.2 Homework 7 Solutions Nov 1 Lp spaces. 5.3 Nov 6 Lp 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. 6.5.2,6.5.37.1 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 2 Practice 3 (Except Question 10).

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