Assess graduate students' understanding of modes of convergence in measure theory: almost everywhere, in measure/probability, in L^p, and in distribution. Tasks include stating precise definitions, proving standard implications (e.g., a.e. + dominated convergence ⇒ L^1; L^p ⇒ convergence in measure), constructing explicit counterexamples for non-implications (e.g., convergence in measure without a.e., L^1 not implying L^2), and applying key results (Dominated Convergence, Riesz, Portmanteau). Emphasize analyzing sequences of measurable functions or random variables to determine which convergences hold and why.