Textbook abbreviations FD = Folland's Real Analysis RD = Royden's Real Analysis EG=Evans Gariepy's Measure theory

Date Topics Sections Event Week 1 9-22       9-24       09-26 Sigma algebra FD 1.1-1.2 Read FD Chapter 0 Week 2 9-29 Measure FD 1.3   10-01 Outer measure FD 1.4   10-03 Borel measures on real line I FD 1.5 Week 3 10-06 Borel measures on real line II FD 1.5 HW1 due 10-08 Measurable functions FD 2.1   10-10 Measurable function and integration FD 2.1-2.2   Week 4 10-13 Integration I FD 2.2-2.3 HW2 due 10-15 Integration II FD 2.3   10-17 Integration III FD 2.4   Week 5 10-20 Product I FD 2.5 HW3 due 10-22 Product II FD 2.5-2.6   10-24 Product III FD 2.6   Week 6 10-27 Polar coordinate FD 2.7 HW4 due 10-29 Review and catch up     10-31 Midterm Exam Midterm Exam Midterm Exam Week 7 11-03 Signed measure I FD 3.1   11-05 Lebesgue-Radon-Nikodym Theorem FD 3.2   11-07 Complex measure FD 3.3   Week 8 11-10 Differentiation I FD 3.4 HW 5 due 11-12 Differentiation II FD 3.4   11-14 Differentiation III FD 3.5   Week 9 11-17 Review and catch up   HW 6 due 11-19 Review and catch up     11-21 Topological space FD 4.1   Week 10 11-24 Topological space and continuous map FD 4.1-4.2 HW 7 due; 11-26 Continuous map FD 4.2   11-28 Thanks giving Thanks giving   Week 11 12-01 Net FD 4.3 HW 8 due; 12-03 Compactness FD 4.4   12-05 Final exam Final exam

Date Topics Sections Event Week 1 01-05 Urysohn's lemma and Tietze Extension Theorem FD 4.2 HW 0 due; 01-07 Net FD 4.3   01-09 Compactness FD 4.4   Week 2 01-12 Locally compact Hausdorff (LCH) FD 4.5 HW 1 due 01-14 Compactness theorems FD 4.6   01-16 Stone-Weierstrass and Stone-Cech compactification FD 4.7-5.8   Week 3 01-19 Happy holiday Happy holiday Happy holiday 01-21 Review/Catch up HW 2 due 01-23 Banach space FD 5.1   Week 4 01-26 Hahn-Banach theorem FD 5.2 01-28 Baire Category Theorem FD 5.3 01-30 Topological Vector Space FD 5.4   Week 5 02-02 Hilbert Spaces FD 5.5 HW 3 due 02-04 Hilbert Spaces II FD 5.5 02-06 Review/catch up   Week 6 02-09 Midterm exam Midterm exam 02-11 L^p space I FD 6.1 HW 4 due 02-13 L^p space II FD 6.2   Week 7 02-16 Happy Holiday Happy Holiday Happy Holiday 02-18 L^p space III FD 6.3 HW 5 due 02-20 Sobolev spaces I EG 4.1, 4.2   Week 8 02-23 Sobolev spaces II EG 4.2 HW 6 due 02-25 Sobolev spaces III EG 4.3 02-27 Sobolev spaces IV EG 4.4   Week 9 03-02 Sobolev spaces V EG 4.5 HW 7 due 03-04 Sobolev spaces VI EG 4.5 03-06 Sobolev spaces VII EG 4.6   Week 10 03-09 Riesz Representation and Compactness for Radon measure I EG 1.8 HW 8 due 03-11 Riesz Representation and Compactness for Radon measure II EG 1.8-1.9 03-13 Riesz Representation and Compactness for Radon measure III EG 1.8-1.9

Date Topics Sections Event Week 1 03-30 Lipschitz functions and Rademancher theorem EG 4.2   04-01 Rademancher theorem and compactness EG 4.2, 4.6   04-03 Compactness EG 4.6   Week 2 04-06 Radon measures I FD 7.1 HW 1 due 04-08 Radon measures II FD 7.2   04-10 Radon measures III EG 1.8   Week 3 04-13 Radon measures IV EG 1.8 HW 2 due 04-15 Review/Catch up     04-17 Distributions I FD 8.1   Week 4 04-20 Distributions II FD 8.2 HW 3 due 04-22 Distributions II FD 9.1 04-24 Review and Catch up     Week 5 04-27 Fourier transform FD 8.3 HW4 due 04-29 Fourier transform II FD 8.3.5   05-01 Review/catch up     Week 6 05-04 Midterm exam Midterm exam 05-06 Hausdorff measures I EG 2.1 HW 5 due 05-08 Hausdorff measures II EG 2.1   Week 7 05-11 Hausdorff measures III EG 2.2   05-13 Hausdorff measure IV EG 2.2 05-15 Hausdorff measures V EG 2.3   Week 8 05-18 Area and Co-area formulae EG 3   05-20 Area and Co-area formulae II EG 3   05-22 Area and Co-area formulae III EG 3

Last modified: Wed Sep 7:06:11 PST 2005