Mathematics 245b, Winter 2003 Classpage
Note: Folland has various corrections for his text on his webpage:
- 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
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