I am looking for an advanced analysis (or, if you prefer, calculus) text that treats in detail the multiple improper Riemann integral, together with the theory of limit passages under the sign of improper multiple integral, and improper multiple integrals with variable singularity and limiting procedures with such integrals (an example of an improper multiple integral with variable singularity would be an integral giving potential of some charge distribution). Any good suggestions?
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I think pretty much any real analysis text dealing with multiple integrals or any of the several dozen "classical type" advanced calculus texts (some of which are listed here) should have what you want. I think if these books aren't what you are looking for, then you should include in your question why they are not, and you'll probably get some suggestions more focused on what you want. Personally, I'd just visit a university library (if one is within reasonable driving distance) and browse the shelves of advanced calculus and analysis books. – Dave L. Renfro Aug 26 '24 at 20:42
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For non-multiple improper Riemann integrals, maybe Improper Riemann Integrals by Ioannis M. Roussos (2014). For multiple integrals, maybe Chapter 17 of Mathematical Analysis II by Vladimir A. Zorich (2016; 2nd edition). – Dave L. Renfro Aug 26 '24 at 20:53