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Problem-solving strategies for integration theory in measure theory
Passed 22 of 22 test cases with the skill, and 18 of 22 without it.
and 1 more in the full report
4 fixed18 passed either way0 still failing0 broke
Tokens, turns and time describe resource use, not a dollar price.
One of 4 test cases the skill fixed. Same model, same prompt, with and without the skill.
What command should be executed to prove that an increasing sequence $f_n$ satisfies the limit exchange property using the automated theorem prover harness?
| Checked | Without skill | With skill |
|---|---|---|
| The response specifies running scripts/z3_solve.py with the prove action for monotone convergence. | Missed | Passed |
The instructions your model reads when the skill loads.
Use this skill when working on integration-theory problems in measure theory.
Simple function integration
sympy_compute.py simplify "simple_integral"Monotone Convergence Theorem (MCT)
Dominated Convergence Theorem (DCT)
z3_solve.py prove "dominated_convergence"Fatou's Lemma
Fubini-Tonelli
uv run python -m runtime.harness scripts/sympy_compute.py integrate "sum(a_i * chi_E_i)" --var mu
test cases passed, vs 18 / 22 without
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