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sigma-algebras

Verify sigma-algebra axioms and function measurability using Z3 and SymPy.

8|1|Updated Jan 4, 2026
Search Tags:#formal verification#mathematics#probability#set theory#measure theory#sigma-algebra
One-click install
npx skills add https://github.com/scooter-lacroix/Maestro --skill sigma-algebras
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: sigma-algebras
Source: https://github.com/scooter-lacroix/Maestro/tree/main/maestro/skills/math/math/measure-theory/sigma-algebras
Command: npx skills add https://github.com/scooter-lacroix/Maestro --skill sigma-algebras

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill includes scripts (resource) and references (resource) components.

What problem does it solve?

This Skill provides strategies and tools for solving problems related to sigma-algebras in measure theory, ensuring mathematical rigor and correctness.

Core Features & Use Cases

  • Axiom Verification: Checks if a given collection of sets satisfies the axioms of a sigma-algebra.
  • Sigma-Algebra Generation: Assists in constructing the smallest sigma-algebra containing a given collection of sets.
  • Measurability Testing: Verifies if a function is measurable with respect to given sigma-algebras.
  • Use Case: When proving theorems in probability or measure theory, this skill helps verify the foundational properties of sigma-algebras and the measurability of functions.

Quick Start

Use the sigma-algebras skill to verify the axioms for a sigma-algebra.

Frequently Asked Questions about sigma-algebras

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I verify if a collection of sets satisfies sigma-algebra axioms?▼

To verify sigma-algebra axioms, this Skill checks closure under complement and countable unions using Z3, ensuring your collection of sets meets measure theory requirements.

What is the best way to generate a sigma-algebra from a given collection of sets?▼

Generating a sigma-algebra is facilitated by this Skill through methods like Dynkin's pi-lambda theorem, helping you construct the smallest sigma-algebra containing your specified sets.

How do I check if a function is measurable with respect to specific sigma-algebras?▼

To check function measurability, this Skill employs symbolic computation with SymPy for preimage analysis, verifying that preimages of measurable sets exist within your target sigma-algebras.

Can I use SymPy and Z3 for formal verification of measure theory properties?▼

Yes, you can use this Skill for formal verification of measure theory properties, leveraging Z3 for deterministic axiom verification and SymPy for symbolic preimage analysis.

Does this tool help with proving theorems in probability theory?▼

Yes, this Skill helps with proving theorems in probability theory by verifying foundational sigma-algebra properties and function measurability, ensuring mathematical rigor in your proofs.

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