Please recommend a problem book with solutions on graduate level real analysis and measure theory

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I'd like to find a problem book (with solutions) about graduate level real analysis (measure theory). That is, at the level of the books by Royden or Zygmund.

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The only book I know that is like that is "Schaum Outline Series: Real variables", but I dont really know the quality of the excercises at all, every other 'Real analysis', problem book I know doesnt include measure theory.

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(1) Bogachev: Measure Theory Volumes I and II.

(2) Bruckner: Real analysis

Cheers.