Measure Theory

The course addresses the Lebesgue measure of subsets of real numbers. The text book is "Real Analysis" of Royden and Fitzpatrick.

Week Fifteen

Here you can find a proof of the existence of a non-measurable set.

Week Thirteen

Here you can find two exercises. Please, also look at exercises 1 and 2 at page 31 of the book.

These are the solutions. And these are the solutions of exercises 1 and 2 of page 31 of the book.

Week Twelve

Here you can find some exercises on the topology of the set of real numbers.

And these are the solutions.

Week Three

Homeworks

Week One

Homeworks

Solutions