integration-theory
Problem-solving strategies for integration theory in measure theory
Profile →npx skills add parcadei/Continuous-Claude-v3 --skill integration-theory --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# Integration Theory ## When to Use Use this skill when working on integration-theory problems in measure theory. ## Decision Tree 1. **Simple function integration** - For s = sum(a_i * chi_{E_i}): integral s dmu = sum(a_i * mu(E_i)) - `sympy_compute.py simplify "simple_integral"` 2. **Monotone Convergence Theorem (MCT)** - If 0 <= f_n <= f_{n+1} and f_n -> f: - lim integral(f_n) = integral(lim f_n) - Use for increasing sequences 3. **Dominated Convergence Theorem (DCT)** - If |f_n| <= g (integrable) and f_n -> f pointwise: - lim integral(f_n) = integral(f) - `z3_solve.py prove "dominated_convergence"` 4. **Fatou's Lemma** - integral(liminf f_n) <= liminf(integral f_n) - Use as lower bound when MCT/DCT don't apply 5. **Fubini-Tonelli** - For product measures: switch order of integration - Tonelli: non-negative functions (always valid) - Fubini: integrable functions ## Tool Commands ### Sympy_Simple_Integral ```bash uv run python -m runtime.harness scripts/sympy_compute.py integrate "sum(a_i * chi_E_i)" --var mu ``` ### Z3_Mct ```bash uv run python -m runtime.harness scripts/z3_solve.py prove "f_n_increasing implies lim_integral_equals_integral_lim" ``` ### Z3_Dct ```bash uv run pyt
- When to Use
- Decision Tree
- Tool Commands
- SympySimpleIntegral
- Z3Mct
- Z3Dct
- SympyFatou
- Key Techniques
- Cognitive Tools Reference
uv run python -m runtime.harness scripts/sympy_compute.py integrate "sum(a_i * chi_E_i)" --var mu uv run python -m runtime.harness scripts/z3_solve.py prove "f_n_increasing implies lim_integral_equals_integral_lim" uv run python -m runtime.harness scripts/z3_solve.py prove "abs(f_n) <= g and g_integrable implies limit_exchange" uv run python -m runtime.harness scripts/sympy_compute.py limit "liminf(integral_f_n)" --comparison "integral_liminf_f_n"
What does the integration-theory skill do?
Problem-solving strategies for integration theory in measure theory
How do I install it?
Run `npx skills add parcadei/Continuous-Claude-v3 --skill integration-theory --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From parcadei/Continuous-Claude-v3, a repository with 3,885 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.