Assess students' ability to state the Dominated Convergence Theorem precisely and apply it to justify interchanging limits and integrals in L^p settings: identify and verify almost-everywhere convergence, find or disprove existence of an integrable dominating function (or appropriate L^p bound), compute limits of integrals for sequences in L^p, and analyze counterexamples where hypotheses fail (including failure of domination or lack of uniform integrability). Tasks include short proofs, verification of hypotheses for concrete sequences and functions, and explanation of when alternative tools (e.g., Vitali convergence theorem) are required.