Can someone please recommend a textbook that gives a substantial treatment of absolute continuity and is accessible (written for students; sticks to the real numbers instead of turning to more abstract generalizations)?
Textbook on absolute continuity
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real-analysis
reference-request
absolute-continuity
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0If you have access to interlibrary loan or ProQuest, you may want to look at Walter Eugene Klann, **Properties and Applications of Absolutely Continuous Functions**, Ed.D. Dissertation (under Donald Dale Elliott), Colorado State College [= University of Northern Colorado], 1968, ix + 190 + 1 pages. I gave a summary of its contents [here](https://math.stackexchange.com/questions/677927/bibliography-for-singular-functions), where it is bibliographic entry **[43]**. – 2017-07-06
2 Answers
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A way more substantial (but still accessible) treatment than the one in Royden's book can be found in Leoni's A First Course in Sobolev Spaces.
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The Wikipedia page on absolute continuity frequently uses Royden, H.L. (1988), Real Analysis (third ed.) as a reference. I think newer editions of this book are co-authored by Fitzpatrick, as Google searching the reference brought me to this pdf. See page 119 in the book numbering, page 130 in the pdf. I hope this helps.
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0If you can find a copy of I. P. Natanson, Theory of functions of a real variable, I think you will be pleased with the treatment. – 2017-01-23