What book would you recommend me to read about measure theory and especially the following:
Measure and outer meansure, Borel sets, the outer Lebesgue measure.
The Cantor set.
Properties of Lebesgue measure (translation invariance, completeness, regularity, uniqueness).
Steinhaus theorem, non-Lebesgue measurable sets.
Measurable functions, integrable functions, convergence theorems.
Elementary theory of Hilbert spaces.
Complex measures, the Radon-Nikodym theorem.
The maximal function Hardy-Littlewood.
Differentiation of measures and functions.
Product of measures. The Fubini theorem.
Change of variable. Polar coordinates. Convolutions.
??
Best Answer
Gerald Folland's Real Analysis book is a superb choice for learning measure theory and elementary functional analysis. It covers all the topics you listed.
It is a bit more difficult and abstract than most other introductory textbook (such as Royden), but it is well worth it (and yes, it is actually suitable for a first-time learner, because I was). If you want a solid foundation on measure theory, this is the single book you should own.