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I study physics in English but at a German university. My current math class roughly follows the book "Königsberger Analysis 2" but I can't find a copy of this in English. I'm kind of in trouble because I don't learn very well from lectures, and only learn from going slowly through a text on my own. Last semester I just tried to revise my notes carefully after each lecture, but it didn't work out so well. So I would be grateful if somebody could recommend me an accessible, yet rigorous, analysis book that deals roughly with the topics of:

Multivariable integral calculus (line integrals, volume integrals etc)

Lebesque Integrals (measure theory)

Complex Analysis

Functional analysis (spaces and operators)

Also, anything that has worked through examples, or questions with solutions is very much welcome.

Thanks

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# Need a good Analysis book

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