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Measure Theory

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

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Week Fifteen

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

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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.

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Week Twelve

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

And these are the solutions.

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Week Three

Homeworks

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Week One

Homeworks

Solutions