Kolmogorov & Fomin's Elements of Theory: Real Analysis or Lebesque?

[zyj]

I'm looking for a Real Analysis book to start with, besides Spivak. On Amazon, one of the reviewers said it was good as a subsequent book for learning Functional Analysis/Lebesque Integration, while another said it was a good introduction to Real Analysis. For those of you that have read it, which is it?

 

[bda23]

I haven't read it in full, I must admit, only started it a while back. But I'd say it is more geared towards functional analysis and Lebesgue. The reason why some readers say it is good for real analysis is probably because it has a chapter on metric spaces. The book overall is not bad, I'd say, but the pace is not leisurely, and you'll have to concentrate a bit more than for some other books. But really, as I said, I haven't read most of the book, so I can't say too much about it. I think if you really want to study functional analysis, some other books might be better, as the functional analysis part in this book is rather modest. But as an introduction in general, it's probably quite good.

 

[zyj]

Do you think I would be able to handle it after or while concurrently reading Spivak?

 

[jbunniii]

I think there's a rather large gap going from Spivak to Kolmogorov and Fomin. That gap is also known as Baby Rudin.

 

[jgens]

Do you think I would be able to handle it after or while concurrently reading Spivak?

It would be reasonable to attempt the book after reading and working through the problems in the calculus text by Spivak.