German Analysis Texts

Solution 1:

I can highly recommend the book

Mass- und Integrationstheorie by Jürgen Elstrodt (Measure theory).

It is the most detailed book I know on this subject. Sometimes it is also a bit too formal, but it serves very well as a reference book (he treats $\sigma$-algebras and similar object in a very detailed manner). Furthermore, in functional analysis I would recommend

Funktionalanalysis by Dirk Werner.

It is a good source of examples and a very well written (also formal) introduction to the subject providing the fundamental definitions and theorems.

Solution 2:

Try the first in the following selection of books; it's for free. It comes with solutions to all exercises.

https://people.math.ethz.ch/~blatter/dlp.html