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The popular texts on Measure Theory that I know of (as well as sone probability texts I have), such as Royden, Folland, and Halmos, seem to not address topics such as atoms, atomic measures, or nonatomic measures other than maybe a page of explanation, or they may just throw such topics in an exercise or two.

I am looking for a textbook to supplement the one-page explanation on Atomic and Nonatomic Measures (section 3.5) in Dudley's Real Analysis and Probability. The textbook should introduce these topics toward the beginning with the intro measure theory sections, around the time when Lebesgue measure is introduced.

Are there any suggestions for such a text? I am particularly looking for more than just defining what atomic/nonatomic measures simply are: I am seeking some exposition on theorems as well.

Clarinetist
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  • Have you seen Fremlin's 5-volume treatise? https://www1.essex.ac.uk/maths/people/fremlin/mt.htm – Unit Oct 18 '20 at 19:45
  • @Unit Thanks, I haven't until now. I'd say Volume 2 is more extensive on its treatment of such concepts, but not by much. Results such as this I've had a very hard time finding in textbooks. – Clarinetist Oct 18 '20 at 20:02

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