Mathematics 245b, Winter 2003 Classpage

• Recitation: Thursday, 2PM, Kinsey 141
• Office hours: Tu, Fri 4-5
• Course grade calculation: 1/4 hour exam, 1/4 homework, 1/2 final
• Late assignments will not be graded
• At the end of the quarter, the lowest assignment grade will be dropped
• NOTE CORRECTION: Hour exam: Wednesday Feb. 12. This will cover material through and including the isoperimetric inequality, as well as assignments 1 and 2.
• Final Exam: Tuesday March 18, 11:30-2:30
• Note ass 4 due on Friday
• REVIEW SESSION MONDAY 10:30-11:30 USUAL ROOM

• Assignment 1: p. 186: 3,4,5,6,7
  Show that if the norm on a Banach space satisfies the parallelogram rule (5.22) then the Banach space is a Hilbert space.
• Assignment 2
  Correction problem 2c: replace x by x^2
• Assignment 3 Due: Mon. Feb. 24 (decided on Wednesday afternoon at the request of members of the course)
  
• Assignment 4: ( due on Friday March 14.)
  1. Prove that a set S in the reals is an interval in the sense we defined in lecture (the in-between-property) if and only if it has the one of the forms (a,b), [a,b), etc. Explain how we used this to show that monotonic functions must be Borel.
  2. Prove that if f is Borel and g=f almost everywhere then g is measurable (you may assume the measure is Lebesgue measure on the reals).
  3. p. 107-8: 30, 37, 38, 39, 40
  

• Solutions to assignment 1
• Solutions to assignment 2.
  Note: Silvius has graded this assignment. The papers are outside his office.
• A review of the proof that monotonic functions have derivatives almost everywhere.