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Math 6312 – Measure Theory – Winter 2006

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					                    Math 6312 – Measure Theory – Winter 2006
                                   Instructor: Dr. Jie Xiao
               Slot: M 11:00-11:50 & T 11:00-12:40 ∼ Room: HH 3017 & C-4042

Overview
• Measure theory is the basis of modern theories of integration, of which Lebesgue integration is
  a special case. The theory is quite general, permitting many notions of integration on a broad
  family of mathematical spaces. It is intimately tied to both functional analysis and geometric
  analysis. This course will provide students with a broad introduction to the subject, with
  certain emphasis on the geometric aspects.
Prerequisite
• The only assumed knowledge will be the elementary real analysis with proofs. However, the
  course will move quickly – some prior exposure to integration, metric space and linear functional
  analysis would be a definite advantage.
Textbook
• Measure Theory and Fine Properties of Functions by L. C. Evans and R. R. Cariepy, CRC
  Press, 1992. Other general texts on measure theory would be worth having on hand. Of
  course, there are many good ones around – to pick two largely at random: Real Analysis by H.
  Royden, Prentice-Hall, 1988; Real Analysis: Modern Techniques and Their Applications by G.
  Folland, John Wiley and Sons, 1999 (2nd edition).
Contents
• General measures; Lebesgue measure and Hausdorff measure; Lusin’s Theorem and Egoroff’s
  Theorem; Limit theorems for integrals; Lp spaces; Product measures and Fubini’s Theorem;
  Radon-Nikodym Theorem; Riesz Representation Theorem; Area and Coarea Formulas; Sobolev
  spaces; Capacities.
• Later topics, subject to time, will include: BV functions; Sets of finite perimeter; Differentia-
  bility; Approximation by C 1 functions.
Grading
• Course grade will be based on homeworks and/or projects assigned biweekly.
Office Hours and Contact Information
• Time: Wednesday 14:00-17:00 or by appointment; Room: HH 3044; Tel: 737-8072; Email:
  jxiao@math.mun.ca; URL: http://www.math.mun.ca/˜jxiao.
Some important Dates
• Jan. 9, Monday - Lectures begin.
• Jan. 23, Monday - Last day to add courses.
• Feb. 20, Monday - Winter Semester Break begins at St. John’s Campus and Sir Wilfred
  Grenfell College.
• Feb. 23, Thursday - Lectures resume at St. John’s Campus and Sir Wilfred Grenfell College.
• Feb. 27, Monday - Last Day for students to drop winter semester courses without academic
  prejudice.
• April 7, Friday - Lectures end for winter semester.
• April 12, Wednesday - Examinations begin for winter semester.
• April 22, Saturday - Examinations end for winter semester.
• April 27, Thursday - Official release of final grades.


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