I generally enjoy Axler's prose, so I am thinking about learning measure theory and the basics of functional analysis from this book. Anyone have any opinions on it?
>>16835098It's handholdy, but accessible. I like it as a self study textbook but I much prefer Folland if you're working with a study group or tutor.
I do like it.In light of it's content amount, it's appropriately concise while spelling things out with a good balance of text and formulas. One could write different measure theory books - and they exist. One could define a dozen set family and set algebra notions, one could could go far with impredicative definitions - but they don't aid as much as other topics in measure theory.The formatting is a lot better than in most books (slight drawback that there's less content _per_ page, but that's a minor thing).I don't like his mindless pledge in favour of Choice, but that's just because I generally care about formal logic (not even so much set theory) more than measure theory.I really dislike his "done right" title, and implied attitude. But again that doesn't take away from the content.tl;dr I think it covers a lot of content, and in a way that you can actually read the book end to end. Good if you e.g. want to understand integral theory for a foundation in probability or Fourier theory. If the contents are a means to you, then I'd def go with it. If not, I might still skim it in 3 afternoons, before going for a more topical/abstract text.
>>16835098Measure theory touts shit like "we define infinity + infinity = infinity" which to me is utter nonsense so i choose to denounce it.
