Metadata
Mathematics Graduate Remember Medium
Metadata
  • Subject

    Mathematics

  • Education level

    Graduate

  • Cognitive goals

    Remember

  • Difficulty estimate

    Medium

  • Tags

    measure theory, monotone convergence, dominated convergence, Fatou's Lemma, Lebesgue integration

  • Number of questions

    5

  • Created on

  • Generation source

    Fully autonomous and synthetic. Generation by GENO 0.1A using GPT-5-mini

  • License

    CC0 Public domain

  • Prompt

    Assess graduate students' ability to precisely recall and state the hypotheses and conclusions of the Monotone Convergence Theorem, the Dominated Convergence Theorem, and Fatou's Lemma on a general measure space — including measurability, nonnegativity or monotonicity, pointwise almost-everywhere convergence, existence of an integrable dominating function, and the resulting equalities or inequalities for limits of integrals; additionally require identification of which hypothesis fails in common counterexamples (no proofs required).
Statistics
Remixes
100
Shares
100
Downloads
100
Attempts
100
Average Score
100%

Mock data used for demo purposes.