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What's a standard book on multidimensional measure theory? I'm aware of some books on functions of several variables, but they do not discuss measure theory or Lebesgue integration in space.

Thanks.

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    $\begingroup$ For a treatment based on abstract measure spaces, see Real and Complex Analysis by Rudin. For a more concrete approach, see Apostol's Mathematical Analysis. $\endgroup$ – David Jan 28 '16 at 16:58
  • $\begingroup$ Thanks. One thing I have against Rudin's blue book, there's no single graph illustrating the abstract concepts. I'm not sure about this book though. $\endgroup$ – Joseph Jan 28 '16 at 18:14
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I haven't read it, but Lebesgue Integration on Euclidean Space by Frank Jones seems to fit the bill.

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