Thread: Vitali Covering Theorem

Hello everyone.

I need some books that cover the Vitali Covering Theorem. Ofcourse there's wikipedia, but I need actul books that take you through the background and details of the proof (via the covering lemma ofcourse). I'm doing a project on this topic. I tried looking for the books that wikipedia lists at my universities library, but they only have the one by Natanson. Natanson's book is quite old, and only deals with subsets of the real line, whereas I need something that deals with R^n or a general metric space.
Btw, I'm still an undergrad.

Thanks.

Originally Posted by qspeechc

Hello everyone.

I need some books that cover the Vitali Covering Theorem. Ofcourse there's wikipedia, but I need actul books that take you through the background and details of the proof (via the covering lemma ofcourse). I'm doing a project on this topic. I tried looking for the books that wikipedia lists at my universities library, but they only have the one by Natanson. Natanson's book is quite old, and only deals with subsets of the real line, whereas I need something that deals with R^n or a general metric space.
Btw, I'm still an undergrad.

Thanks.

We just covered this in my real analysis class. I liked the proof in our text book. Real Analysis N.L. Carothers. When I did a google book search pg 287 was not part of the preview( this is the first half of the proof) but pg 288 is. You can look at least half of it to see if it is what you are looking for.