Curriculum Spring 2023

The curriculum that you should be familiar with in connection with the final exam this spring consists of the material covered during the lectures (except the one on May 16) and the exercises sessions, see the notes and solutions available in the schedule for the course. Here is an overview of the topics which are relevant for the exam, with references to the literature. 

From Lindstr?m's book ?Spaces?: 

Sections 7.1 - 7.6 and 7.9 

Sections 8.1 - 8.4

In section 7.2, the proof of Theorem 7.2.5 (which include Lemmas 7.2.2-7.2.4) was not covered; you need only to know what this theorem says.  

In section 8.2, we only sketched the proof of Theorem 8.2.6; you don¡¯t have to spend time scrutinizing all the details in this proof. 

In section 8.4, we did not cover the example following Prop. 8.4.6 about non-measurable sets.

From Brevig¡¯s note ?A measure of Lebesgue measure?: 

Chapter 1, 2 and 3

Note that when comparing Riemann integration vs Lebesgue integration, our presentation was closer to Lindstr?m¡¯s presentation in section 7.5 than the one given in Brevig¡¯s section 1.1.

From the notes on Elementary Linear Analysis:

Chapters 1 - 3 and sections 4.1 - 4.3

 In section 2.1, we skipped the proof of Proposition 2.1.4, so don¡¯t worry about it.

In section 3.1, we only proved Theorem 4.1.6 in the case where Y is a Hilbert space H (this result follows from Theorem 4.2.1 in this case).