New: 98,000+ skills indexed from GitHub repos with 100+ stars · every skill safety-checkedBrowse top skillsTop skills
Esc to closeBrowse all skills
Submit a skillBrowse skills
Submit a skillBrowse skills

Agent skill

Sigma Algebras

by parcadei in parcadei/Continuous-Claude-v3

Problem-solving strategies for sigma algebras in measure theory

MITAuto-check: notesResearch & Science

Install Sigma Algebras

skills CLI
$ npx skills add parcadei/Continuous-Claude-v3 --skill sigma-algebras -a claude-code

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

GitHub CLI
$ gh skill install parcadei/Continuous-Claude-v3 sigma-algebras --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/sigma-algebras .claude/skills/sigma-algebras && 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
sigma-algebras
GitHub stars
3.9k
Used in
1 other repo
Token cost
~784 tokens
SKILL.md length
387 words
Files
1
Skills in repo
141
Repo updated
First seen
Licence
MIT

At a glance

Problem-solving strategies for sigma algebras in measure theory

  • Works in 4 steps: Verify sigma-algebra axioms → sigma-algebra generation → Measurability verification → …
  • 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

Sigma Algebras is an agent skill from parcadei/Continuous-Claude-v3. Problem-solving strategies for sigma algebras in measure theory

Its SKILL.md is about 780 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. 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

  • “/sigma-algebras”

Requirements

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

Workflow steps

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

  1. Verify sigma-algebra axioms
  2. sigma-algebra generation
  3. Measurability verification
  4. Product sigma-algebras

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

Sigma Algebras loads about 784 tokens when it runs. Until then it costs about 20 tokens; SKILL.md has 387 words of instructions outside code blocks.

Always · name and description, kept in context so the agent knows when to use it
~20
When it runs · the whole SKILL.md, loaded when a task matches
~784

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). 387 words, ~784 tokens.

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

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 scripts/sympy_compute.py simplify "f_inv(A_union_B) == f_inv(A) | f_inv(B)"

Key Techniques

From indexed textbooks:

  • [Statistical Inference (George Casella... (Z-Library)] PROBABILITY THEORY Definition 1. A collection of subsets of S is called a sigma algebra (or Borel field), denoted by B, if it satisfies the following three properties: a. B (the empty set is an element of B).
  • [Measure, Integration Real Analysis (... (Z-Library)] S T is the smallest s-algebra containing the measurable rectangles). S T The technique outlined above should be used when possible. However, in some situations there seems to be no reasonable way to verify that the collection of sets with the desired property is a s-algebra.
  • [Statistical Inference (George Casella... (Z-Library)] Thus, again by property (b), N2, A; € B. Associated with sample space § we can have many different sigma algebras. For example, the collection of the two sets {#, S} is a sigma algebra, usually called the trivial sigma algebra.
  • [Real Analysis (Halsey L. Royden, Patr... (Z-Library)] Proposition 13 Let F be a collection of subsets of a set X. Then the intersection A of all σ-algebras of subsets of X that contain F is a σ-algebra that contains F. Moreover, it is the smallest σ-algebra of subsets of X that contains F, in the sense that any σ-algebra that contains F also contains A.
  • [Real Analysis (Halsey L. Royden, Patr... (Z-Library)] Let M be the collection of subsets of X that are either countable or have a countable complement in X. For E ∈ M, dene µ(E) = 0 if E is countable and µ(E) = 1, if E has a countable complement. Is this measure space complete?
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/sigma-algebras 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

Sigma Algebras 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.

Sigma Algebras compared with similar skills
SkillStarsUsed inTokensAuto-checkLicenceRepo updated
Sigma Algebras this skillparcadei/Continuous-Claude-v33.9k1 repos~784Automated safety check: NotesMIT
Hypothesis Generationspacering-net/codeg3.9k14 repos~3.6kAutomated safety check: NotesMIT
GitHub Deep Researchbytedance/deer-flow84k4 repos~1.3kAutomated safety check: PassMIT
Nature Paper CardYuan1z0825/nature-skills47k2 repos~2.1kAutomated safety check: PassApache-2.0
Content Research Writerweapp-tailwindcss/weapp-tailwindcss1.9k25 repos~3.5kAutomated safety check: PassMIT
Last30daysmvanhorn/last30days-skill64k—~7.9kAutomated safety check: NotesMIT

Similar skills

  • Hypothesis Generation

    spacering-net/codeg

    Structured hypothesis formulation from observations. An agent skill from spacering-net/codeg.

    3.9k GitHub starsUsed in 14 repos~3.6k tokens
    Research & ScienceAuto-check: notes

  • GitHub Deep Research

    bytedance/deer-flow

    Researches a GitHub repository over four rounds using the GitHub API and web search, then writes a structured markdown report with timeline, metrics and Mermaid diagrams.

    84k GitHub starsUsed in 4 repos~1.3k tokens
    Research & ScienceAuto-check passed

  • Nature Paper Card

    Yuan1z0825/nature-skills

    Builds a structured deep-reading card for one scientific paper, covering methods, how experiments support claims, limitations and research ideas, with a script to prepare the source.

    47k GitHub starsUsed in 2 repos~2.1k tokens
    Research & ScienceAuto-check passed

  • Content Research Writer

    weapp-tailwindcss/weapp-tailwindcss

    Assists in writing high-quality content by conducting research, adding citations, improving hooks, iterating on outlines, and providing real-time feedback on each section.

    1.9k GitHub starsUsed in 25 repos~3.5k tokens
    Research & ScienceAuto-check passed

  • Last30days

    mvanhorn/last30days-skill

    Research what people actually say about any topic in the last 30 days.

    64k GitHub stars~7.9k tokensUpdated yesterday
    Research & ScienceAuto-check: notes

  • Peer Review

    spacering-net/codeg

    Structured manuscript/grant review with checklist-based evaluation.

    3.9k GitHub starsUsed in 17 repos~5.9k tokens
    Research & ScienceAuto-check: notes

More from parcadei/Continuous-Claude-v3

All 141 skills in this repo

  • Compound Learnings

    parcadei/Continuous-Claude-v3

    Transform session learnings into permanent capabilities (skills, rules, agents).

    3.9k GitHub starsUsed in 1 repo~1.6k tokens
    Auto-check: notes

  • Debug Hooks

    parcadei/Continuous-Claude-v3

    Systematic hook debugging workflow. An agent skill from parcadei/Continuous-Claude-v3.

    3.9k GitHub starsUsed in 1 repo~863 tokens
    Auto-check: notes

  • Tldr Deep

    parcadei/Continuous-Claude-v3

    Full 5-layer analysis of a specific function. An agent skill from parcadei/Continuous-Claude-v3.

    3.9k GitHub starsUsed in 1 repo~677 tokens
    Auto-check passed

  • Gradient Methods

    parcadei/Continuous-Claude-v3

    Problem-solving strategies for gradient methods in optimization

    3.9k GitHub starsUsed in 2 repos~1k tokens
    Auto-check: notes

  • Math

    parcadei/Continuous-Claude-v3

    Unified math capabilities - computation, solving, and explanation.

    3.9k GitHub starsUsed in 2 repos~1.6k tokens
    Auto-check: notes

  • Math Model Selector

    parcadei/Continuous-Claude-v3

    Routes problems to appropriate mathematical frameworks using expert heuristics

    3.9k GitHub starsUsed in 2 repos~841 tokens
    Auto-check passed

Categories

Questions about Sigma Algebras

What does Sigma Algebras do?

Problem-solving strategies for sigma algebras in measure theory. Sigma Algebras is an agent skill from parcadei/Continuous-Claude-v3.

When should I use Sigma Algebras?

Sigma Algebras fits situations like: research & Science work in your project.

How do I install Sigma Algebras in Claude Code?

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

How do I install Sigma Algebras in Codex?

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

Can I use Sigma Algebras 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 sigma-algebras -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/sigma-algebras, .gemini/skills/sigma-algebras, .github/skills/sigma-algebras and .opencode/skills/sigma-algebras in your project.

What does Sigma Algebras need to run?

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

Does Sigma Algebras 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 Sigma Algebras 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 Sigma Algebras use?

Sigma Algebras 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 Sigma Algebras use?

About 784 tokens (SKILL.md is roughly 3.1k 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 Sigma Algebras?

Skills that share tags, products or a category with Sigma Algebras: Hypothesis Generation (spacering-net/codeg, 3.9k stars), GitHub Deep Research (bytedance/deer-flow, 84k stars), Nature Paper Card (Yuan1z0825/nature-skills, 47k stars) and Content Research Writer (weapp-tailwindcss/weapp-tailwindcss, 1.9k stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.

Who maintains Sigma Algebras?

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.