September 20-21

This week, we started with the proof of Theorem 3.5 and reached to Example 4.5.1. Also, I solved the Exercises 3.3 and 3.5. At additional Exercise hour, I solved Exercises 2.37, 3.4 and in order to give you a notion to see that larger sets than open sets  may also be Borel sets, I provided a sketch of the related part of the solution of the Exercise 1.2. In the book, at page 4, for the solution of Exercise 1.2, it claims that "we need only show, they generate the open intervals.", which is a wrong/half assertion. Hence, for the sake of completeness and for the possibility of being confused for whom follow the book as well, I will upload the complete solution today.

Tentative plan of the next week is starting with Definition 4.8 and following the book closely up to the end of the proof of Dominated convergence theorem. Planned exercises are 3.19, 2.40, 2.41, 2.42.

There will be an additional exercise hour on Tuesday, 28.09.2021, 17: 00-18: 00 - Niels Henrik Abels hus Undervisningsrom 1020.