Beskjeder
EXAM: The oral exam will be on Thursday June 10, starting 10 a.m.
EKSAMEN: Dato for muntlig eksamen er torsdag 10. juni, fra kl. 10:00.
Comment on E 4.2.5. Every linear surjection from a topological vector space onto complex n-space C^n is open. However, this result does not apply to the map of the hint: The character space is no vector space.
Comments on E 2.5.5 (b).
The result of this exercise holds only for "sufficiently regular" measures, such as Lebesgue measure on Euclidean space R^n. Otherwise counter examples can easily be constructed. Let for instance c be counting measure on the sigma algebra S generated by two disjoint singletons {x} and {y} in X={x,y}. Thus S={?,X,{x},{y}}. Then the characteristic function f of {x} (and of {y}) is an extreme point on the closed unit ball B of L^1. Show this!
The same argument applies to the counting measure on the (infinite) sigma algebra of all subsets of a set of any countable collection of distinct points, X={x(1),...,x(n),...}. The characteristic function of each one-point set {x(k)} ( 1≤k ) is an extreme point in the closed unit ball of L^1. Other examples are obtained whenever there is a point x in X such that the set {x} has positive measure.
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ANOTHER CHANGE OF TIME.
Starting the coming week, our new (and I hope final) schedule will be:
Wednesday 1415-1600, B63 (lecture)
Friday 1415-1600, B62 (lecture and problem session)
Consequently, there will be no lecture on Monday February 1.
Exercise E 2.2.4 in Analysis Now:
More details on the solution, in particular that || T_n||=||D_n||_1, can be found here
CHANGE OF TIME AND PLACE.
Starting Monday January 25, the new time schedule will be:
Monday 1015-1200, B62 (lecture)
Wednesday 1415-1600, B63 (lecture and problem session)
Welcome to MAT 4350!
We start the course on Monday January 18 with Section 2.2 in the book Analysis Now, by G. K. Pedersen.
We will also discuss possible changes of the given time schedule.