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lebesgue-measure

Compute Lebesgue outer measures with Sympy and verify Caratheodory criteria using Z3.

3.9k|296|Updated Dec 23, 2025
Search Tags:#mathematics#measure theory#z3#sympy#lebesgue measure#outer measure#caratheodory criterion
One-click install
npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill lebesgue-measure-parcadei
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: lebesgue-measure
Source: https://github.com/parcadei/Continuous-Claude-v3/tree/main/.claude/skills/math/measure-theory/lebesgue-measure
Command: npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill lebesgue-measure-parcadei

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill requires sympy, z3, and includes scripts (resource) and references (resource) components.

What problem does it solve?

This Skill provides strategies and tools for solving problems related to Lebesgue measure in measure theory, simplifying complex mathematical concepts.

Core Features & Use Cases

  • Outer Measure Construction: Utilizes Sympy to calculate outer measures based on interval coverings.
  • Caratheodory Criterion: Employs Z3 solver to prove or verify the Caratheodory criterion for measurability.
  • Lebesgue Measure Properties: Outlines key properties like translation invariance and sigma-additivity.
  • Use Case: When faced with a problem requiring the calculation of the measure of a complex set or proving its measurability, this skill offers direct computational and logical tools.

Quick Start

Use the lebesgue-measure skill to compute the outer measure of a set using Sympy.

Frequently Asked Questions about lebesgue-measure

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

FAQPage Schema
How do I calculate the Lebesgue outer measure of a complex set?▼

Calculate the Lebesgue outer measure of a complex set by using Sympy for symbolic computation to evaluate interval coverings. This provides direct computational tools for measure theory problems.

How can I verify the Caratheodory criterion for measurability using Z3?▼

Verify the Caratheodory criterion for measurability by employing the Z3 solver to construct and automate logical proofs. This validates whether a given set satisfies the required measurable conditions.

What is the best way to prove Lebesgue measure properties like translation invariance?▼

Prove Lebesgue measure properties like translation invariance and sigma-additivity by leveraging Z3 for logical proofs and Sympy for symbolic computation. These tools provide direct strategies for property verification.

Do I need Sympy and Z3 to solve measure theory problems with this approach?▼

Yes, you need Sympy and Z3 to solve measure theory problems with this approach. Sympy handles symbolic computation for outer measure construction, while Z3 automates logical proofs for the Caratheodory criterion.

Does Sympy support calculating the outer measure based on interval coverings?▼

Yes, Sympy supports calculating the outer measure based on interval coverings. It is utilized specifically to compute and evaluate the outer measure construction for complex sets in measure theory.

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