Functional Analysis by Riesz and Sz.-Nagy

[micromass]

• Author: Frigyes Riesz, Bela Sz.-Nagy
• Title: Functional Analysis
• Amazon link: https://www.amazon.com/dp/0486662896/?tag=pfamazon01-20

 

[mathwonk]

To me, this book's explanation of Lebesgue integration is one of the clearest and simplest available. They do it without measure theory first, then give also the version with measures, due to Lebesgue himself. Finally they mention some alternatives. I have used this discussion to explain integration and antidifferentiation as simply as I could in post #9 of the following thread.

https://www.physicsforums.com/showthread.php?t=668367

But see also posts #12 and #14 where I try to modify some possibly erroneous remarks about question #3 discussed there, which I have been unable to edit out.