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Agent skill

Lebesgue Measure

by parcadei in parcadei/Continuous-Claude-v3

Problem-solving strategies for lebesgue measure in measure theory

MITAuto-check: notesResearch & Science

Install Lebesgue Measure

skills CLI
$ npx skills add parcadei/Continuous-Claude-v3 --skill lebesgue-measure -a claude-code

Project install by default; add -g for ~/.claude/skills/.

GitHub CLI
$ gh skill install parcadei/Continuous-Claude-v3 lebesgue-measure --agent claude-code

Project scope by default; add --scope user for a personal install. Needs GitHub CLI 2.90.0 or later (public preview).

Manual copy
$ git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git skills-src && mkdir -p .claude/skills && cp -r skills-src/.claude/skills/math/measure-theory/lebesgue-measure .claude/skills/lebesgue-measure && rm -rf skills-src

Use ~/.claude/skills/ instead of .claude/skills for a personal install. The folder must contain SKILL.md.

Claude Code skills documentation · loads skills from .claude/skills/

Facts

Skill name
lebesgue-measure
GitHub stars
3.9k
Used in
1 other repo
Token cost
~827 tokens
SKILL.md length
415 words
Files
1
Skills in repo
141
Repo updated
First seen
Licence
MIT

At a glance

Problem-solving strategies for lebesgue measure in measure theory

  • Works in 4 steps: Outer measure construction → Caratheodory criterion → Lebesgue measure properties → …
  • Research & Science work in your project
  • SKILL.md covers When to Use, Decision Tree, Tool Commands and Key Techniques, plus 1 more section
  • Calls uv

What it does

Lebesgue Measure is an agent skill from parcadei/Continuous-Claude-v3. Problem-solving strategies for lebesgue measure in measure theory

Its SKILL.md is about 830 tokens, which your agent loads only when the skill is triggered. It is a single SKILL.md file with no bundled scripts.

It sits in Research & Science. It works with SymPy. The repository describes itself as: Context management for Claude Code. Hooks maintain state via ledgers and handoffs. MCP execution without context pollution. Agent orchestration with isolated context windows. The licence is MIT.

When your agent uses it

  • Research & Science work in your project

Example prompts

  • “/lebesgue-measure”

Requirements

  • Python 3
  • Pre-approved tools (allowed-tools): Bash, Read

Workflow steps

4 steps, taken from the first numbered list in SKILL.md.

  1. Outer measure construction
  2. Caratheodory criterion
  3. Lebesgue measure properties
  4. Regularity theorems

What it can do on your machine

Read from SKILL.md and the folder at commit d07ff4b. It shows what the files ask for, not the result of running them.

  • Tool permissions

    Pre-approves these tools, so the agent can use them without asking each time:

    • Bash
    • Read

    From allowed-tools in the SKILL.md frontmatter.

  • Runs code

    Shell commands in SKILL.md call:

    • uv

    From the folder's file list and the shell code blocks in SKILL.md.

  • Network

    No URLs in SKILL.md. Its commands use uv, which can reach the network depending on how they are called.

    From URLs in SKILL.md, links to its own repository left out.

  • Credentials

    Names no API keys, tokens, secrets or passwords.

    From names ending in _API_KEY, _TOKEN, _SECRET, _KEY or _PASSWORD in SKILL.md.

Context cost

Lebesgue Measure loads about 827 tokens when it runs. Until then it costs about 21 tokens; SKILL.md has 415 words of instructions outside code blocks.

Always · name and description, kept in context so the agent knows when to use it
~21
When it runs · the whole SKILL.md, loaded when a task matches
~827

Estimates: characters ÷ 4, the usual rule of thumb; real counts depend on the model's tokenizer. Scripts and assets cost tokens only if the agent reads them.

Safety

Auto-check: notes

The automated check noted patterns worth knowing about, such as sudo or a known installer.

  • NotePre-approves every shell command (allowed-tools: Bash)SKILL.md
    allowed-tools: Bash, Read

Automated static check — not a guarantee. Review scripts before installing. It scans the text of SKILL.md for risky patterns (piping downloads into a shell, reading credential files, hidden Unicode, destructive commands); files beside SKILL.md are not scanned.

SKILL.md

The full file from parcadei/Continuous-Claude-v3 at commit d07ff4b, republished under its MIT licence (© parcadei). 415 words, ~827 tokens.

Download SKILL.mdSave it as .claude/skills/lebesgue-measure/SKILL.md (or your agent's skills folder).
name
lebesgue-measure
description
Problem-solving strategies for lebesgue measure in measure theory
allowed-tools
Bash, Read

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 measure on the Lebesgue measurable sets does have one small advantage over Lebesgue measure on the Borel sets: every subset of a set with (outer) measure 0 is Lebesgue measurable but is not necessarily a Borel set. However, any natural process that produces a subset of R will produce a Borel set. Thus this small advantage does not often come up in practice.
  • [Measure, Integration Real Analysis (... (Z-Library)] B j j You have probably long suspected that not every subset of R is a Borel set. Now j j j j Section 2D Lebesgue Measure restricted to the Borel sets, is a measure. Borel sets Outer measure is a measure on (R, of R.
  • [Measure, Integration Real Analysis (... (Z-Library)] The terminology Lebesgue set would make good sense in parallel to the termi- nology Borel set. However, Lebesgue set has another meaning, so we need to use Lebesgue measurable set. Every Lebesgue measurable set differs from a Borel set by a set with outer measure 0.
  • [Measure, Integration Real Analysis (... (Z-Library)] If you go at a leisurely pace, then covering Chapters 1–5 in the rst semester may be a good goal. If you go a bit faster, then covering Chapters 1–6 in the rst semester may be more appropriate. For a second-semester course, covering some subset of Chapters 6 through 12 should produce a good course.
  • [Measure, Integration Real Analysis (... (Z-Library)] Egorov’s Theorem, which states that pointwise convergence of a sequence of measurable functions is close to uniform convergence, has multiple applications in later chapters. Luzin’s Theorem, back in the context of R, sounds spectacular but has no other uses in this book and thus can be skipped if you are pressed for time. Chapter 4: The highlight of this chapter is the Lebesgue Differentiation Theorem, which allows us to differentiate an integral.
Show full SKILL.md (9 more words)Show less

Cognitive Tools Reference

See .claude/skills/math-mode/SKILL.md for full tool documentation.

© parcadei, MIT. Rendered from Markdown: HTML in the file is shown as text, images as links, and headings moved down two levels. Raw file

Files

Just SKILL.md in .claude/skills/math/measure-theory/lebesgue-measure of parcadei/Continuous-Claude-v3.

Open the folder on GitHubat commit d07ff4b

Used in 1 other repository

We found 1 copy of this SKILL.md (exact, near-identical or edited) in other folders, from 1 other GitHub owner. This page covers the copy in parcadei/Continuous-Claude-v3, which our catalogue first saw on October 7, 2026.

Compare with similar skills

Lebesgue Measure next to the 5 skills that share the most tags, products or categories with it. Stars are the repository's; “used in” counts other GitHub owners with a copy.

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Works with

Categories

Questions about Lebesgue Measure

What does Lebesgue Measure do?

Problem-solving strategies for lebesgue measure in measure theory. Lebesgue Measure is an agent skill from parcadei/Continuous-Claude-v3.

When should I use Lebesgue Measure?

Lebesgue Measure fits situations like: research & Science work in your project.

How do I install Lebesgue Measure in Claude Code?

Run `npx skills add parcadei/Continuous-Claude-v3 --skill lebesgue-measure -a claude-code`. Or copy the skill folder (.claude/skills/math/measure-theory/lebesgue-measure in parcadei/Continuous-Claude-v3) into .claude/skills/lebesgue-measure in your project. Claude Code loads it when a task matches its description.

How do I install Lebesgue Measure in Codex?

Run `npx skills add parcadei/Continuous-Claude-v3 --skill lebesgue-measure -a codex`. Or copy the skill folder (.claude/skills/math/measure-theory/lebesgue-measure in parcadei/Continuous-Claude-v3) into .agents/skills/lebesgue-measure in your project. Codex loads it when a task matches its description.

Can I use Lebesgue Measure in Cursor, Gemini CLI or GitHub Copilot?

Cursor, Gemini CLI, GitHub Copilot and OpenCode also load SKILL.md folders. With the skills CLI, run `npx skills add parcadei/Continuous-Claude-v3 --skill lebesgue-measure -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/lebesgue-measure, .gemini/skills/lebesgue-measure, .github/skills/lebesgue-measure and .opencode/skills/lebesgue-measure in your project.

What does Lebesgue Measure need to run?

Going by SKILL.md and its folder, Lebesgue Measure needs the command-line tools its instructions call (uv). Our summary lists: Python 3. Its frontmatter pre-approves these tools: Bash, Read.

Does Lebesgue Measure access the network?

SKILL.md contains no URLs. Its commands use uv, which can reach the network depending on how they are called. This is read from the text; nothing was executed.

Is Lebesgue Measure safe to install?

Our automated static check of SKILL.md found notes only (pre-approves every shell command (allowed-tools: bash)), nothing it rates as a warning. It is not a guarantee. Review the folder before installing.

What licence does Lebesgue Measure use?

Lebesgue Measure is published under the MIT licence (the repository's licence). It allows redistribution, so the full SKILL.md is shown on this page.

How many tokens does Lebesgue Measure use?

About 827 tokens (SKILL.md is roughly 3.3k characters). Agents keep only the skill's name and description in context until a task matches; then they load SKILL.md in full.

What are the alternatives to Lebesgue Measure?

Skills that share tags, products or a category with Lebesgue Measure: Sympy (zLanqing/codex-claude-academic-skills, 4.7k stars), Edu Analytic Geometry (wy51ai/edulab, 1.4k stars), Edu Solid Geometry (wy51ai/edulab, 1.4k stars) and Math Tools (ananddtyagi/cc-marketplace, 687 stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.

Who maintains Lebesgue Measure?

parcadei (a GitHub user) maintains it in parcadei/Continuous-Claude-v3, which has 3,943 GitHub stars. The repository holds 141 skills in this directory. The repository was last updated on January 26, 2026.

Source: parcadei/Continuous-Claude-v3 on GitHub. Facts on this page come from the repository at the commit we read; the author's words are quoted as theirs.