Metadata
Mathematics Graduate Remember Medium
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Metadata

  • Subject

    Mathematics

  • Education level

    Graduate

  • Cognitive goals

    Remember

  • Difficulty estimate

    Medium

  • Tags

    measure theory, monotone convergence, dominated convergence, Fatou's Lemma, Radon–Nikodym, 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 state the Monotone Convergence Theorem, Dominated Convergence Theorem, Fatou's Lemma, and the Radon–Nikodym Theorem: include required measure-space assumptions, integrability/positivity conditions, almost-everywhere convergence hypotheses, exact conclusions about limits of integrals or existence of densities, and note standard counterexamples when hypotheses fail.
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Remixes
100
Shares
100
Downloads
100
Attempts
100
Average Score
100%

Mock data used for demo purposes.