Assess students' ability to analyze and prove or disprove implications among convergence modes in L^p(X,μ)—pointwise a.e., convergence in measure, almost uniform, convergence in L^p norm, and weak convergence. Tasks: identify which implications hold under common hypotheses (e.g., finite measure, dominated convergence, uniform integrability, reflexivity), supply rigorous proofs when true, and construct explicit counterexamples when implications fail, noting dependence on p and on properties of the measure space.