npx skills add parcadei/Continuous-Claude-v3 --skill sigma-algebras --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.
# Sigma Algebras ## When to Use Use this skill when working on sigma-algebras problems in measure theory. ## Decision Tree 1. **Verify sigma-algebra axioms** - X in F (whole space is measurable) - A in F implies A^c in F (closed under complements) - A_n in F implies union(A_n) in F (closed under countable unions) - `z3_solve.py prove "sigma_algebra_axioms"` 2. **sigma-algebra generation** - Start with generating collection C - sigma(C) = smallest sigma-algebra containing C - Use Dynkin's pi-lambda theorem for uniqueness 3. **Measurability verification** - f is measurable if f^{-1}(B) in F for all Borel B - Sufficient: check for open sets or intervals - `sympy_compute.py simplify "preimage(f, interval)"` 4. **Product sigma-algebras** - F1 x F2 = sigma{A x B : A in F1, B in F2} - Projections are measurable ## Tool Commands ### Z3_Sigma_Axioms ```bash uv run python -m runtime.harness scripts/z3_solve.py prove "X_in_F and closed_under_complement and closed_under_countable_union" ``` ### Z3_Dynkin_Pi_Lambda ```bash uv run python -m runtime.harness scripts/z3_solve.py prove "pi_system_subset_lambda implies sigma_equal" ``` ### Sympy_Preimage ```bash uv run python -m runtime.harness scrip
- When to Use
- Decision Tree
- Tool Commands
- Z3SigmaAxioms
- Z3DynkinPiLambda
- SympyPreimage
- Key Techniques
- Cognitive Tools Reference
uv run python -m runtime.harness scripts/z3_solve.py prove "X_in_F and closed_under_complement and closed_under_countable_union" uv run python -m runtime.harness scripts/z3_solve.py prove "pi_system_subset_lambda implies sigma_equal" uv run python -m runtime.harness scripts/sympy_compute.py simplify "f_inv(A_union_B) == f_inv(A) | f_inv(B)"
What does the sigma-algebras skill do?
Problem-solving strategies for sigma algebras in measure theory
How do I install it?
Run `npx skills add parcadei/Continuous-Claude-v3 --skill sigma-algebras --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.