MCT, DCT, and Fatou's Lemma related problems Bank

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One of my friends is preparing for his Analysis Ph.D. comprehensive exam. He requested me to give him a list of problems that can be solved using the three standard convergence theorems namely MCT, DCT, and FL. I have already collected some problems from some standard textbooks. Can you please recommend me more problems? I think it will be helpful for many other students.

Thank you so much.