lebesgue-measure
Problem-solving strategies for lebesgue measure in measure theory
Profile →npx skills add parcadei/Continuous-Claude-v3 --skill lebesgue-measure --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.
# Lebesgue Measure ## When to Use Use this skill when working on lebesgue-measure problems in measure theory. ## Decision Tree 1. **Outer measure construction** - m*(A) = inf{sum |I_n| : A subset union(I_n)} - `sympy_compute.py sum "length(I_n)" --var n` 2. **Caratheodory criterion** - E is measurable if: m*(A) = m*(A & E) + m*(A & E^c) for all A - `z3_solve.py prove "caratheodory_criterion"` 3. **Lebesgue measure properties** - Translation invariant: m(E + x) = m(E) - sigma-additive on measurable sets - m([a,b]) = b - a 4. **Regularity theorems** - Inner regularity: m(E) = sup{m(K) : K compact, K subset E} - Outer regularity: m(E) = inf{m(U) : U open, E subset U} ## Tool Commands ### Sympy_Outer_Measure ```bash uv run python -m runtime.harness scripts/sympy_compute.py sum "length(I_n)" --var n --from 1 --to oo ``` ### Z3_Caratheodory ```bash uv run python -m runtime.harness scripts/z3_solve.py prove "mu(A) == mu(A & E) + mu(A & E_complement)" ``` ### Sympy_Borel_Sets ```bash uv run python -m runtime.harness scripts/sympy_compute.py simplify "open_set_countable_union" ``` ## Key Techniques *From indexed textbooks:* - [Measure, Integration Real Analysis (... (Z-Library)] Lebesgue me
- When to Use
- Decision Tree
- Tool Commands
- SympyOuterMeasure
- Z3Caratheodory
- SympyBorelSets
- Key Techniques
- Cognitive Tools Reference
uv run python -m runtime.harness scripts/sympy_compute.py sum "length(I_n)" --var n --from 1 --to oo uv run python -m runtime.harness scripts/z3_solve.py prove "mu(A) == mu(A & E) + mu(A & E_complement)" uv run python -m runtime.harness scripts/sympy_compute.py simplify "open_set_countable_union"
What does the lebesgue-measure skill do?
Problem-solving strategies for lebesgue measure in measure theory
How do I install it?
Run `npx skills add parcadei/Continuous-Claude-v3 --skill lebesgue-measure --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.